Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
Re: Olympic question(s)
82 views
Skip to first unread message
R H Draney
Aug 18, 2012, 4:55:10 AM8/18/12
to
Guy Barry filted:
>
>More seriously, has anyone ever commented on the irregular formation of
>words like "billion", "trillion" and so on? They appear to contain the
>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
>indicates an enlargement or augmentation.
Another instance of "-orama syndrome" (also known as "the -teria
principle")....r
--
Me? Sarcastic?
Yeah, right.
>
>More seriously, has anyone ever commented on the irregular formation of
>words like "billion", "trillion" and so on? They appear to contain the
>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
>indicates an enlargement or augmentation.
Another instance of "-orama syndrome" (also known as "the -teria
principle")....r
--
Me? Sarcastic?
Yeah, right.
CDB
Aug 18, 2012, 6:42:02 AM8/18/12
to
On 18/08/2012 3:47 AM, pauljk wrote:
[illions and illions]
> I imagine zillion termites crawling in a line, while gazillion
> of them would be a two-dimensional carpet of termites covering
> the lawn. :-)
Not to mention your brazillion thriller termites. Please.
[illions and illions]
> I imagine zillion termites crawling in a line, while gazillion
> of them would be a two-dimensional carpet of termites covering
> the lawn. :-)
Not to mention your brazillion thriller termites. Please.
Peter T. Daniels
Aug 18, 2012, 9:27:06 AM8/18/12
to
On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> Surely the area of a 1-meter line segment is 0, so it's not
> incommensurate with the area of a square 1 meter on a side.
Surely there's a difference between a dimension of 0 and complete
nonexistence -- a 1-meter line segment has no area, so a fortiori it
doesn't have an area of 0.
> Surely the area of a 1-meter line segment is 0, so it's not
> incommensurate with the area of a square 1 meter on a side.
Surely there's a difference between a dimension of 0 and complete
nonexistence -- a 1-meter line segment has no area, so a fortiori it
doesn't have an area of 0.
Joachim Pense
Aug 18, 2012, 10:27:54 AM8/18/12
to
geometrical figures.
I would not think you can say "X has no area" when you mean to say "The
notion "area" doesn't apply to X, as in *"the color red has no area".
Joachim
Jerry Friedman
Aug 18, 2012, 10:54:52 AM8/18/12
to
On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:
> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> >> Surely the area of a 1-meter line segment is 0, so it's not
> >> incommensurate with the area of a square 1 meter on a side.
>
> > Surely there's a difference between a dimension of 0 and complete
> > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > doesn't have an area of 0.
>
> "No area" is another way to say "an area of 0", when applied to
> geometrical figures.
...
> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> >> Surely the area of a 1-meter line segment is 0, so it's not
> >> incommensurate with the area of a square 1 meter on a side.
>
> > Surely there's a difference between a dimension of 0 and complete
> > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > doesn't have an area of 0.
>
> "No area" is another way to say "an area of 0", when applied to
> geometrical figures.
Just as "no money" is another way to say "a net worth of 0", and "The
neutron has no charge" is another way to say "The neutron has a charge
of 0."
If you're interested in a more formal approach, Peter, you might want
to look up "set of measure 0".
--
Jerry Friedman
Paul Wolff
Aug 18, 2012, 11:02:25 AM8/18/12
to
In message <slrnk2t395....@mbp55.local>, Lewis
<g.k...@gmail.com.dontsendmecopies> writes
>In message <k0lg98$q9v$1...@dont-email.me>
> pauljk <paul....@xtra.co.nz> wrote:
>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>
>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>
>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>> of an area?
>>>
>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>bigger than a
>>> zillion then :-)
>
>> That's not what I said, read it again.
>> Square X is just a different unit than X.
>> For instance, one square metre is still only one metre, it's
>> an area of one square metre, unlike plain metre which is
>> a distance of one metre.
>
>A square meter is much larger than a meter. Infinitely so, in fact. A
>cubic meter is much larger than a square meter too, and even larger than
>a meter, but still infinitely larger than both.
>
It's clear to me that a square meter is one meter times greater than a
linear meter, and a cubic meter one meter times greater than a square
meter.
--
Paul
<g.k...@gmail.com.dontsendmecopies> writes
>In message <k0lg98$q9v$1...@dont-email.me>
> pauljk <paul....@xtra.co.nz> wrote:
>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>
>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>
>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>> of an area?
>>>
>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>bigger than a
>>> zillion then :-)
>
>> That's not what I said, read it again.
>> Square X is just a different unit than X.
>> For instance, one square metre is still only one metre, it's
>> an area of one square metre, unlike plain metre which is
>> a distance of one metre.
>
>A square meter is much larger than a meter. Infinitely so, in fact. A
>cubic meter is much larger than a square meter too, and even larger than
>a meter, but still infinitely larger than both.
>
It's clear to me that a square meter is one meter times greater than a
linear meter, and a cubic meter one meter times greater than a square
meter.
--
Paul
Peter T. Daniels
Aug 18, 2012, 11:30:29 AM8/18/12
to
On Aug 18, 10:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > >> Surely the area of a 1-meter line segment is 0, so it's not
> > >> incommensurate with the area of a square 1 meter on a side.
>
> > > Surely there's a difference between a dimension of 0 and complete
> > > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > > doesn't have an area of 0.
>
> > "No area" is another way to say "an area of 0", when applied to
> > geometrical figures.
>
> ...
>
> Just as "no money" is another way to say "a net worth of 0",
Not the same at all. A thing with a net worth of 0 can easily become a
> On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > >> Surely the area of a 1-meter line segment is 0, so it's not
> > >> incommensurate with the area of a square 1 meter on a side.
>
> > > Surely there's a difference between a dimension of 0 and complete
> > > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > > doesn't have an area of 0.
>
> > "No area" is another way to say "an area of 0", when applied to
> > geometrical figures.
>
> ...
>
> Just as "no money" is another way to say "a net worth of 0",
thing with a net worth of any other cash equivalent, but a thing with
no area cannot become a thing with an area of 0 (or any other value).
> and "The
> neutron has no charge" is another way to say "The neutron has a charge
> of 0."
> If you're interested in a more formal approach, Peter, you might want
> to look up "set of measure 0".
Hmm, is there more than one empty set? Is the set of all unicorns the
same as the set of all living people 150 years old?
Evan Kirshenbaum
Aug 18, 2012, 11:50:47 AM8/18/12
to
Lewis <g.k...@gmail.com.dontsendmecopies> writes:
> In message <has119...@gmail.com>
>> than a meter?
>
> ∞ > 0
>
> Any is infinitely larger than none.
A square meter has volume?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |Yesterday I washed a single sock.
SF Bay Area (1982-) |When I opened the door, the machine
Chicago (1964-1982) |was empty.
evan.kir...@gmail.com
http://www.kirshenbaum.net/
> In message <has119...@gmail.com>
> Evan Kirshenbaum <evan.kir...@gmail.com> wrote:
>> Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>>> In message <k0lg98$q9v$1...@dont-email.me>
>>> pauljk <paul....@xtra.co.nz> wrote:
>>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>>
>>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>>>
>>>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>>>> of an area?
>>>>>
>>>>> I hadn't thought of that! A zillion times a zillion. Definitely bigger than a
>>>>> zillion then :-)
>>>
>>>> That's not what I said, read it again.
>>>> Square X is just a different unit than X.
>>>> For instance, one square metre is still only one metre, it's
>>>> an area of one square metre, unlike plain metre which is
>>>> a distance of one metre.
>>>
>>> A square meter is much larger than a meter. Infinitely so, in fact. A
>>> cubic meter is much larger than a square meter too, and even larger than
>>> a meter, but still infinitely larger than both.
>
>> How would you go about showing that a square meter had more volume
>> Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>>> In message <k0lg98$q9v$1...@dont-email.me>
>>> pauljk <paul....@xtra.co.nz> wrote:
>>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>>
>>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>>>
>>>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>>>> of an area?
>>>>>
>>>>> I hadn't thought of that! A zillion times a zillion. Definitely bigger than a
>>>>> zillion then :-)
>>>
>>>> That's not what I said, read it again.
>>>> Square X is just a different unit than X.
>>>> For instance, one square metre is still only one metre, it's
>>>> an area of one square metre, unlike plain metre which is
>>>> a distance of one metre.
>>>
>>> A square meter is much larger than a meter. Infinitely so, in fact. A
>>> cubic meter is much larger than a square meter too, and even larger than
>>> a meter, but still infinitely larger than both.
>
>> than a meter?
>
> ∞ > 0
>
> Any is infinitely larger than none.
A square meter has volume?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |Yesterday I washed a single sock.
SF Bay Area (1982-) |When I opened the door, the machine
Chicago (1964-1982) |was empty.
evan.kir...@gmail.com
http://www.kirshenbaum.net/
Evan Kirshenbaum
Aug 18, 2012, 11:52:17 AM8/18/12
to
Jerry Friedman <jerry_f...@yahoo.com> writes:
> On Aug 17, 3:32 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> wrote:
>> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
>> > In message <k0lg98$q9...@dont-email.me>
>> > pauljk <paul.kr...@xtra.co.nz> wrote:
>> >> "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote in message
>> >>news:b_kXr.687426$GO2.5...@fx05.am4...
>>
>> >>> "pauljk" wrote in messagenews:k0kbhj$gli$1...@dont-email.me...
"A cubic meter is much larger than a square meter too, and even larger
than a meter". If that's not "larger" in the sense of "has more
volume", then in what sense is it?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |On a scale of one to ten...
SF Bay Area (1982-) |it sucked.
Chicago (1964-1982)
evan.kir...@gmail.com
http://www.kirshenbaum.net/
> On Aug 17, 3:32 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> wrote:
>> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
>> > In message <k0lg98$q9...@dont-email.me>
>> > pauljk <paul.kr...@xtra.co.nz> wrote:
>> >> "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote in message
>> >>news:b_kXr.687426$GO2.5...@fx05.am4...
>>
>> >>> "pauljk" wrote in messagenews:k0kbhj$gli$1...@dont-email.me...
>>
>> >>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>> >>>> of an area?
>>
>> >>> I hadn't thought of that! A zillion times a zillion. Definitely bigger than a
>> >>> zillion then :-)
>>
>> >> That's not what I said, read it again.
>> >> Square X is just a different unit than X.
>> >> For instance, one square metre is still only one metre, it's
>> >> an area of one square metre, unlike plain metre which is
>> >> a distance of one metre.
>>
>> > A square meter is much larger than a meter. Infinitely so, in fact. A
>> > cubic meter is much larger than a square meter too, and even larger than
>> > a meter, but still infinitely larger than both.
>
> Paging Paul "Curlytop" Townsend.
>> >>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>> >>>> of an area?
>>
>> >>> I hadn't thought of that! A zillion times a zillion. Definitely bigger than a
>> >>> zillion then :-)
>>
>> >> That's not what I said, read it again.
>> >> Square X is just a different unit than X.
>> >> For instance, one square metre is still only one metre, it's
>> >> an area of one square metre, unlike plain metre which is
>> >> a distance of one metre.
>>
>> > A square meter is much larger than a meter. Infinitely so, in fact. A
>> > cubic meter is much larger than a square meter too, and even larger than
>> > a meter, but still infinitely larger than both.
>
>
>> How would you go about showing that a square meter had more volume
>> than a meter?
>
> I don't see where anybody said it did.
>> How would you go about showing that a square meter had more volume
>> than a meter?
>
"A cubic meter is much larger than a square meter too, and even larger
volume", then in what sense is it?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |On a scale of one to ten...
SF Bay Area (1982-) |it sucked.
Chicago (1964-1982)
evan.kir...@gmail.com
http://www.kirshenbaum.net/
Evan Kirshenbaum
Aug 18, 2012, 11:56:17 AM8/18/12
to
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |The law of supply and demand tells us
SF Bay Area (1982-) |that when the price of something is
Chicago (1964-1982) |artificially set below market level,
|there will soon be none of that thing
evan.kir...@gmail.com |left--as you may have noticed the
|last time you tried to buy something
http://www.kirshenbaum.net/ |for nothing.
| P.J. O'Rourke
Joachim Pense
Aug 18, 2012, 12:23:29 PM8/18/12
to
Am 18.08.2012 17:30, schrieb Peter T. Daniels:
> On Aug 18, 10:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>> On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>>
>>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>>> Surely there's a difference between a dimension of 0 and complete
>>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>>> doesn't have an area of 0.
>>
>>> "No area" is another way to say "an area of 0", when applied to
>>> geometrical figures.
>>
>> ...
>>
>> Just as "no money" is another way to say "a net worth of 0",
>
> Not the same at all. A thing with a net worth of 0 can easily become a
> thing with a net worth of any other cash equivalent, but a thing with
> no area cannot become a thing with an area of 0 (or any other value).
>
A line can easily become a square, you just have to extend it into that
> On Aug 18, 10:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>> On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>>
>>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>>> Surely there's a difference between a dimension of 0 and complete
>>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>>> doesn't have an area of 0.
>>
>>> "No area" is another way to say "an area of 0", when applied to
>>> geometrical figures.
>>
>> ...
>>
>> Just as "no money" is another way to say "a net worth of 0",
>
> Not the same at all. A thing with a net worth of 0 can easily become a
> thing with a net worth of any other cash equivalent, but a thing with
> no area cannot become a thing with an area of 0 (or any other value).
>
direction. Just like the money.
>> and "The
>> neutron has no charge" is another way to say "The neutron has a charge
>> of 0."
>
>
>
>> If you're interested in a more formal approach, Peter, you might want
>> to look up "set of measure 0".
>
> I'm not; is that the measure of an/the empty set?
>
plane is a less trivial one. The set of all points in a square with only
rational coordinates is an even less trivial one.
Joachim
Message has been deleted
Joachim Pense
Aug 18, 2012, 12:25:18 PM8/18/12
to
Am 18.08.2012 17:52, schrieb Evan Kirshenbaum:
>
> "A cubic meter is much larger than a square meter too, and even larger
> than a meter". If that's not "larger" in the sense of "has more
> volume", then in what sense is it?
>
It is. A square meter has volume zero, and a cubic meter has a volume
>
> "A cubic meter is much larger than a square meter too, and even larger
> than a meter". If that's not "larger" in the sense of "has more
> volume", then in what sense is it?
>
of, er, one cubic meter.
Joachim
Jerry Friedman
Aug 18, 2012, 12:26:01 PM8/18/12
to
On Aug 18, 9:52 am, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
wrote:
I took it to be, "A cubic meter has volume, which makes it much larger
than a square meter, which only has area, and even more larger [*]
than a meter, which only has length."
This doesn't make mathematical sense if you're talking about volume,
since as you say, both the square meter and the linear meter have a
volume of 0. It comes closer to making sense if you're talking about
area and think of the cube as having infinite area. I don't think
mathematicians think of cubical volumes as having area, though.
(In another sense, you could say the cube has an area of 6 m^2.)
[*] Or "largerer".
--
Jerry Friedman
wrote:
than a square meter, which only has area, and even more larger [*]
than a meter, which only has length."
This doesn't make mathematical sense if you're talking about volume,
since as you say, both the square meter and the linear meter have a
volume of 0. It comes closer to making sense if you're talking about
area and think of the cube as having infinite area. I don't think
mathematicians think of cubical volumes as having area, though.
(In another sense, you could say the cube has an area of 6 m^2.)
[*] Or "largerer".
--
Jerry Friedman
Paul Wolff
Aug 18, 2012, 12:28:52 PM8/18/12
to
In message <zk5sxk...@gmail.com>, Evan Kirshenbaum
<evan.kir...@gmail.com> writes
I wouldn't mind if it were less. The principle would still be
established.
--
Paul
<evan.kir...@gmail.com> writes
established.
--
Paul
Guy Barry
Aug 18, 2012, 1:41:27 PM8/18/12
to
"Joachim Pense" wrote in message news:a99tve...@mid.individual.net...
metre. Therefore, by this reasoning, a square metre is larger (in area)
than a cubic metre.
This is a pointless discussion because people are trying to compare apples
with oranges. You can compare two dimensionless quantities, or two lengths,
or two areas, or two volumes. Comparing two items with different dimensions
is meaningless. Which is more, a metre or a kilogram?
--
Guy Barry
Joachim Pense
Aug 18, 2012, 12:42:45 PM8/18/12
to
Am 18.08.2012 18:26, schrieb Jerry Friedman:
>
> This doesn't make mathematical sense if you're talking about volume,
> since as you say, both the square meter and the linear meter have a
> volume of 0. It comes closer to making sense if you're talking about
> area and think of the cube as having infinite area. I don't think
> mathematicians think of cubical volumes as having area, though.
>
I would say "It doesn't make sense to speak of the area of a cube"; I
>
> This doesn't make mathematical sense if you're talking about volume,
> since as you say, both the square meter and the linear meter have a
> volume of 0. It comes closer to making sense if you're talking about
> area and think of the cube as having infinite area. I don't think
> mathematicians think of cubical volumes as having area, though.
>
would avoid saying "A cube has no area", because that could be
misinterpreted as "A cube has area zero".
Joachim
Joachim Pense
Aug 18, 2012, 12:46:13 PM8/18/12
to
Am 18.08.2012 19:41, schrieb Guy Barry:
>
>
> "Joachim Pense" wrote in message news:a99tve...@mid.individual.net...
>
>> Am 18.08.2012 17:52, schrieb Evan Kirshenbaum:
>
>>
>> > "A cubic meter is much larger than a square meter too, and even larger
>> > than a meter". If that's not "larger" in the sense of "has more
>> > volume", then in what sense is it?
>>
>
>> It is. A square meter has volume zero, and a cubic meter has a volume
>> of, er, one cubic meter.
>
> A cubic metre has area zero, and a square metre has area of one square
> metre. Therefore, by this reasoning, a square metre is larger (in area)
> than a cubic metre.
>
> This is a pointless discussion because people are trying to compare
> apples with oranges. You can compare two dimensionless quantities, or
> two lengths, or two areas, or two volumes. Comparing two items with
> different dimensions is meaningless. Which is more, a metre or a kilogram?
>
of height zero.
Joachim
Jerry Friedman
Aug 18, 2012, 12:48:41 PM8/18/12
to
On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> On Aug 18, 10:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> > On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > > > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > > >> Surely the area of a 1-meter line segment is 0, so it's not
> > > >> incommensurate with the area of a square 1 meter on a side.
>
> > > > Surely there's a difference between a dimension of 0 and complete
> > > > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > > > doesn't have an area of 0.
>
> > > "No area" is another way to say "an area of 0", when applied to
> > > geometrical figures.
>
> > ...
>
> > Just as "no money" is another way to say "a net worth of 0",
>
> Not the same at all. A thing with a net worth of 0 can easily become a
> thing with a net worth of any other cash equivalent, but a thing with
> no area cannot become a thing with an area of 0 (or any other value).
>
> > and "The
> > neutron has no charge" is another way to say "The neutron has a charge
> > of 0."
> > If you're interested in a more formal approach, Peter, you might want
> > to look up "set of measure 0".
>
> I'm not;
Okay. If you were, you could figure out why your objection above
> On Aug 18, 10:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> > On Aug 18, 8:27 am, Joachim Pense <s...@pense-mainz.eu> wrote:> Am 18.08.2012 15:27, schrieb Peter T. Daniels:
>
> > > > On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > > >> Surely the area of a 1-meter line segment is 0, so it's not
> > > >> incommensurate with the area of a square 1 meter on a side.
>
> > > > Surely there's a difference between a dimension of 0 and complete
> > > > nonexistence -- a 1-meter line segment has no area, so a fortiori it
> > > > doesn't have an area of 0.
>
> > > "No area" is another way to say "an area of 0", when applied to
> > > geometrical figures.
>
> > ...
>
> > Just as "no money" is another way to say "a net worth of 0",
>
> Not the same at all. A thing with a net worth of 0 can easily become a
> thing with a net worth of any other cash equivalent, but a thing with
> no area cannot become a thing with an area of 0 (or any other value).
>
> > and "The
> > neutron has no charge" is another way to say "The neutron has a charge
> > of 0."
> > If you're interested in a more formal approach, Peter, you might want
> > to look up "set of measure 0".
>
> I'm not;
isn't valid (along the lines of what Joachim Pense said).
> is that the measure of an/the empty set?
>
> Hmm, is there more than one empty set? Is the set of all unicorns the
> same as the set of all living people 150 years old?
there might be some non-standard approach or non-mathematical approach
with different empty sets.)
--
Jerry Friedman
Guy Barry
Aug 18, 2012, 1:55:26 PM8/18/12
to
"Paul Wolff" wrote in message news:M3fuHVRE...@fpwolff.demon.co.uk...
metre were less than one, how could one square metre be greater than one
metre? You're simply multiplying each side of the inequality by one metre,
a positive quantity. (Unless you believe that one metre is negative, of
course; but then a cubic metre would be less than a square metre.)
--
Guy Barry
Guy Barry
Aug 18, 2012, 2:00:08 PM8/18/12
to
"Joachim Pense" wrote in message news:a99v6l...@mid.individual.net...
Anyway, I think I'm better off staying out of this thread, because most of
it is drivel.
--
Guy Barry
GordonD
Aug 18, 2012, 1:55:52 PM8/18/12
to
"R H Draney" <dado...@spamcop.net> wrote in message
news:k0nl9...@drn.newsguy.com...
Is that anything like adding "-gate" to a noun to describe a scandal of some
sort (after Watergate, even though that was the name of the hotel and had
nothing to do with water), or "-holic" to indicate that you are very fond of
something (usually seen as chocoholic)?
--
Gordon Davie
Edinburgh, Scotland
"Slipped the surly bonds of Earth...to touch the face of God."
news:k0nl9...@drn.newsguy.com...
sort (after Watergate, even though that was the name of the hotel and had
nothing to do with water), or "-holic" to indicate that you are very fond of
something (usually seen as chocoholic)?
--
Gordon Davie
Edinburgh, Scotland
"Slipped the surly bonds of Earth...to touch the face of God."
Evan Kirshenbaum
Aug 18, 2012, 2:31:18 PM8/18/12
to
Lewis <g.k...@gmail.com.dontsendmecopies> writes:
> In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
> How is 0 mass different from no mass? 0 means none. 0 length is no
> length, and zero area is no area.
I can't decide whether or not I think that a line doesn't have area or
whether it has area zero, but I agree with Peter that they're
different. Does a line have a mass of zero? A temperature of zero?
What's it's color? How loud is it?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |I value writers such as Fiske.
SF Bay Area (1982-) |They serve as valuable object
Chicago (1964-1982) |lessons by showing that the most
|punctilious compliance with the
evan.kir...@gmail.com |rules of usage has so little to do
|with either writing or thinking
http://www.kirshenbaum.net/ |well.
| --Richard Hershberger
> In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
> length, and zero area is no area.
I can't decide whether or not I think that a line doesn't have area or
whether it has area zero, but I agree with Peter that they're
different. Does a line have a mass of zero? A temperature of zero?
What's it's color? How loud is it?
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |I value writers such as Fiske.
SF Bay Area (1982-) |They serve as valuable object
Chicago (1964-1982) |lessons by showing that the most
|punctilious compliance with the
evan.kir...@gmail.com |rules of usage has so little to do
|with either writing or thinking
http://www.kirshenbaum.net/ |well.
| --Richard Hershberger
Evan Kirshenbaum
Aug 18, 2012, 2:34:34 PM8/18/12
to
is one square meter "even larger" in the second comparison than in the
first? That's what I was objecting to.
--
Evan Kirshenbaum +------------------------------------
Paul Wolff
Aug 18, 2012, 2:33:29 PM8/18/12
to
In message <0OPXr.1344172$3s1....@fx12.am4>, Guy Barry
<guy....@blueyonder.co.uk> writes
I meant only that if one [item] was not greater than another, but less,
then the principle that they could be compared in a ratio would still
have been established, and all that was left to argue about would be the
proportion.
I know it's make-believe. It's a hot August day, and what else do you
expect a fellow to do?
--
Paul
<guy....@blueyonder.co.uk> writes
then the principle that they could be compared in a ratio would still
have been established, and all that was left to argue about would be the
proportion.
I know it's make-believe. It's a hot August day, and what else do you
expect a fellow to do?
--
Paul
Vinny Burgoo
Aug 18, 2012, 3:03:19 PM8/18/12
to
In alt.usage.english, Guy Barry wrote:
>"Paul Wolff" wrote in message news:M3fuHVRE...@fpwolff.demon.co.uk...
>> In message <zk5sxk...@gmail.com>, Evan Kirshenbaum
>"Paul Wolff" wrote in message news:M3fuHVRE...@fpwolff.demon.co.uk...
>> In message <zk5sxk...@gmail.com>, Evan Kirshenbaum
>> >Paul Wolff <boun...@two.wolff.co.uk> writes:
>> >> It's clear to me that a square meter is one meter times greater than a
>> >> linear meter, and a cubic meter one meter times greater than a square
>> >> meter.
>>
>> >Now all you have to do is show that one meter is greater than one.
>>
>> I wouldn't mind if it were less. The principle would still be established.
>
>I hesitate to get involved in such a meaningless discussion
Would you prefer a comparison of the diameter of the thread of fuel
>> >> It's clear to me that a square meter is one meter times greater than a
>> >> linear meter, and a cubic meter one meter times greater than a square
>> >> meter.
>>
>> >Now all you have to do is show that one meter is greater than one.
>>
>> I wouldn't mind if it were less. The principle would still be established.
>
>I hesitate to get involved in such a meaningless discussion
required by a car versus that required by a marathon runner in miles per
gallon per miles per miles per miles (or something: my brain hurts
again)?
http://quantumfrontiers.com/2012/08/10/universal-thread/
It turns out that the thread of gasoline powering an inefficient car has
about the same diameter as the thread of junk food (eww!) powering an
inefficient marathon runner.
--
VB
H/T Quark Soup
Joachim Pense
Aug 18, 2012, 3:20:02 PM8/18/12
to
Am 18.08.2012 20:34, schrieb Evan Kirshenbaum:
>
> Taking that approach, a meter has volume zero, too, so in what sense
> is one square meter "even larger" in the second comparison than in the
> first? That's what I was objecting to.
>
Joachim
R H Draney
Aug 18, 2012, 3:32:58 PM8/18/12
to
Evan Kirshenbaum filted:
"none" as above....r
--
Me? Sarcastic?
Yeah, right.
>
>Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>>In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
>> Peter T. Daniels <gram...@verizon.net> wrote:
>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>> Surely there's a difference between a dimension of 0 and complete
>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>> doesn't have an area of 0.
>>
>> How is 0 mass different from no mass? 0 means none. 0 length is no
>> length, and zero area is no area.
>
>I can't decide whether or not I think that a line doesn't have area or
>whether it has area zero, but I agree with Peter that they're
>different. Does a line have a mass of zero? A temperature of zero?
>What's it's color? How loud is it?
That last question is equivalent to "what's its volume?" so either "zero" or
>Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>>In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
>> Peter T. Daniels <gram...@verizon.net> wrote:
>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>> Surely there's a difference between a dimension of 0 and complete
>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>> doesn't have an area of 0.
>>
>> How is 0 mass different from no mass? 0 means none. 0 length is no
>> length, and zero area is no area.
>
>I can't decide whether or not I think that a line doesn't have area or
>whether it has area zero, but I agree with Peter that they're
>different. Does a line have a mass of zero? A temperature of zero?
>What's it's color? How loud is it?
"none" as above....r
--
Me? Sarcastic?
Yeah, right.
Nathan Sanders
Aug 18, 2012, 3:52:03 PM8/18/12
to
In article
<9ab84467-8ef7-4f0a...@x3g2000vbn.googlegroups.com>,
moment in time), yes (ignoring, of course, the use of "unicorn" to
describe unicorn-shaped toys and other images and approximations of
"real" unicorns).
Intensionally, no (since sentences like "I want to meet a unicorn" and
"I want to meet a living 150-year-old person" are not logically
equivalent, because a given speaker may wish to meet one but not the
other).
Nathan
--
Department of Linguistics
Swarthmore College
http://sanders.phonologist.org/
<9ab84467-8ef7-4f0a...@x3g2000vbn.googlegroups.com>,
> Hmm, is there more than one empty set? Is the set of all unicorns the
> same as the set of all living people 150 years old?
Extensionally (at least in this particular universe at this particular
> same as the set of all living people 150 years old?
moment in time), yes (ignoring, of course, the use of "unicorn" to
describe unicorn-shaped toys and other images and approximations of
"real" unicorns).
Intensionally, no (since sentences like "I want to meet a unicorn" and
"I want to meet a living 150-year-old person" are not logically
equivalent, because a given speaker may wish to meet one but not the
other).
Nathan
--
Department of Linguistics
Swarthmore College
http://sanders.phonologist.org/
Peter T. Daniels
Aug 18, 2012, 4:34:24 PM8/18/12
to
On Aug 18, 1:55 pm, "GordonD" <g.da...@btinternet.com> wrote:
> "R H Draney" <dadoc...@spamcop.net> wrote in messagenews:k0nl9...@drn.newsguy.com...
Yes, it's exactly the same principle and it is, clearly, quite common.
> "R H Draney" <dadoc...@spamcop.net> wrote in messagenews:k0nl9...@drn.newsguy.com...
>
> > Guy Barry filted:
>
> >>More seriously, has anyone ever commented on the irregular formation of
> >>words like "billion", "trillion" and so on? They appear to contain the
> >>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
> >>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
> >>indicates an enlargement or augmentation.
>
> > Another instance of "-orama syndrome" (also known as "the -teria
> > principle")....r
>
> Is that anything like adding "-gate" to a noun to describe a scandal of some
> sort (after Watergate, even though that was the name of the hotel and had
> nothing to do with water), or "-holic" to indicate that you are very fond of
> something (usually seen as chocoholic)?
Of course it has to do with water. Look at the map!
> > Guy Barry filted:
>
> >>More seriously, has anyone ever commented on the irregular formation of
> >>words like "billion", "trillion" and so on? They appear to contain the
> >>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
> >>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
> >>indicates an enlargement or augmentation.
>
> > Another instance of "-orama syndrome" (also known as "the -teria
> > principle")....r
>
> Is that anything like adding "-gate" to a noun to describe a scandal of some
> sort (after Watergate, even though that was the name of the hotel and had
> nothing to do with water), or "-holic" to indicate that you are very fond of
> something (usually seen as chocoholic)?
Yes, it's exactly the same principle and it is, clearly, quite common.
Peter T. Daniels
Aug 18, 2012, 4:37:23 PM8/18/12
to
dimension.
An area is, by definition, a property of things with two dimensions.
Therefore, a line segment cannot have an area (and it is thus
meaningless to assign any number at all to "the area of a line
segment").
Peter T. Daniels
Aug 18, 2012, 4:42:16 PM8/18/12
to
meter can just as easily be conceptualized as a sphere of a certain
radius, and its surface area is presumably not 6 m^2. (There's a pi in
there somewhere, and a 4/3, IIRC from 10th-grade geometry.)
Joachim Pense
Aug 18, 2012, 5:57:50 PM8/18/12
to
Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>>
>> Okay. If you were, you could figure out why your objection above
>> isn't valid (along the lines of what Joachim Pense said).
>
> No. A line segment is, by definition, a thing with one and only one
> dimension.
>
> An area is, by definition, a property of things with two dimensions.
>
> Therefore, a line segment cannot have an area (and it is thus
> meaningless to assign any number at all to "the area of a line
> segment").
>
An area is, by definition, a property of _subsets_ of spaces with two
>>
>> Okay. If you were, you could figure out why your objection above
>> isn't valid (along the lines of what Joachim Pense said).
>
> No. A line segment is, by definition, a thing with one and only one
> dimension.
>
> An area is, by definition, a property of things with two dimensions.
>
> Therefore, a line segment cannot have an area (and it is thus
> meaningless to assign any number at all to "the area of a line
> segment").
>
dimensions (like planes). Lines and points are such subsets, having area
zero. A cube is not a subset of a two-dimensional space.
Joachim
Yusuf B Gursey
Aug 18, 2012, 5:39:28 PM8/18/12
to
On Aug 18, 9:27 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > Surely the area of a 1-meter line segment is 0, so it's not
> > incommensurate with the area of a square 1 meter on a side.
>
> Surely there's a difference between a dimension of 0 and complete
> nonexistence -- a 1-meter line segment has no area, so a fortiori it
> doesn't have an area of 0.
I agree with you.
>
> > Surely the area of a 1-meter line segment is 0, so it's not
> > incommensurate with the area of a square 1 meter on a side.
>
> Surely there's a difference between a dimension of 0 and complete
> nonexistence -- a 1-meter line segment has no area, so a fortiori it
> doesn't have an area of 0.
Jerry Friedman
Aug 18, 2012, 7:34:15 PM8/18/12
to
On Aug 18, 12:31 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
wrote:
> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
> > In message <73180ee6-f2f2-4a9d-af16-b9bf8c39c...@z6g2000vbc.googlegroups.com>
zero. Or just with area = length x width, you get 1 m x 0.
> but I agree with Peter that they're different.
I'd say there are three cases, one of which occurs only in recondite
math. The first case is the area of, for example, the imperfect
subjunctive in Spanish. The idea is nonsense, since the imperfect
subjunctive isn't a subset of a two- or higher-dimensional space or a
physical object satisfactorily approximated by such a subset; it has
nothing to do with area.
The second case is a line segment. If we apply any mathematical
definition of area (that I know of and understand) to it, we get a
well-defined answer of 0.
The third case is sets of points like the subsets of the surface of a
sphere in the Banach-Tarski theorem. These sets are not measurable;
their area can't be defined mathematically. (The existence of the
sets follows from the axiom of choice, and I'm way out of my depth
here.)
> Does a line have a mass of zero? A temperature of zero?
> What's it's color?
Green. ("So paint it green.")
> How loud is it?
When it's whistling?
http://en.wikipedia.org/wiki/The_Joys_of_Yiddish
Mathematical lines have nothing to do with mass, temperature, color,
or loudness, but they can be sets of points in two or more dimensions,
so their area can be defined.
--
Jerry Friedman is agreeing with Joachim Pense a lot here.
wrote:
> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
> > In message <73180ee6-f2f2-4a9d-af16-b9bf8c39c...@z6g2000vbc.googlegroups.com>
> > Peter T. Daniels <gramma...@verizon.net> wrote:
> >> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> >>> Surely the area of a 1-meter line segment is 0, so it's not
> >>> incommensurate with the area of a square 1 meter on a side.
>
> >> Surely there's a difference between a dimension of 0 and complete
> >> nonexistence -- a 1-meter line segment has no area, so a fortiori it
> >> doesn't have an area of 0.
>
> > How is 0 mass different from no mass? 0 means none. 0 length is no
> > length, and zero area is no area.
>
> I can't decide whether or not I think that a line doesn't have area or
> whether it has area zero,
With the usual definition of area in math, as an integral, it has area
> >> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> >>> Surely the area of a 1-meter line segment is 0, so it's not
> >>> incommensurate with the area of a square 1 meter on a side.
>
> >> Surely there's a difference between a dimension of 0 and complete
> >> nonexistence -- a 1-meter line segment has no area, so a fortiori it
> >> doesn't have an area of 0.
>
> > How is 0 mass different from no mass? 0 means none. 0 length is no
> > length, and zero area is no area.
>
> I can't decide whether or not I think that a line doesn't have area or
> whether it has area zero,
zero. Or just with area = length x width, you get 1 m x 0.
> but I agree with Peter that they're different.
math. The first case is the area of, for example, the imperfect
subjunctive in Spanish. The idea is nonsense, since the imperfect
subjunctive isn't a subset of a two- or higher-dimensional space or a
physical object satisfactorily approximated by such a subset; it has
nothing to do with area.
The second case is a line segment. If we apply any mathematical
definition of area (that I know of and understand) to it, we get a
well-defined answer of 0.
The third case is sets of points like the subsets of the surface of a
sphere in the Banach-Tarski theorem. These sets are not measurable;
their area can't be defined mathematically. (The existence of the
sets follows from the axiom of choice, and I'm way out of my depth
here.)
> Does a line have a mass of zero? A temperature of zero?
> What's it's color?
> How loud is it?
When it's whistling?
http://en.wikipedia.org/wiki/The_Joys_of_Yiddish
Mathematical lines have nothing to do with mass, temperature, color,
or loudness, but they can be sets of points in two or more dimensions,
so their area can be defined.
--
Jerry Friedman is agreeing with Joachim Pense a lot here.
António Marques
Aug 18, 2012, 8:13:55 PM8/18/12
to
of type X is not generally replaceable with an array of type Y, even
if both are empty.
And you can add elements to an empty set or values to a numeric object
of value 0, whereas you can't do anything with a null set or a null
number. The point here is that even if you dismiss these as artefacts
of notation or memory management, they do serve purposes. For
instance, you can have a function the purpose of which is to determine
the position of the first occurrence of a character in a string. If
the character isn't part of the string, it's not correct to reply '0'.
The usual solution to problems like these has been to reply '-1',
which will sort of worjk as long as all the valid replies are
positive; however, the elegant and meaningful reply would be 'null'.
And boolean values? True is 'yes', false is 'no'. What is null? The
correct thing to consider is that it means 'undetermined'.
For me, if you say a 'line segment' has an area of 0, I'll consider
that you're in fact talking about a closed polygon with at least one
side of length 0. Otherwise, take a triangle and remove one of the
sides. What does 'area' mean when applied to the remaining shape?
António Marques
Aug 18, 2012, 8:21:25 PM8/18/12
to
On Aug 19, 12:34 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> Mathematical lines have nothing to do with mass, temperature, color,
> or loudness, but they can be sets of points in two or more dimensions,
> so their area can be defined.
I think what you're saying is that there is a way to define 'area' so
> Mathematical lines have nothing to do with mass, temperature, color,
> or loudness, but they can be sets of points in two or more dimensions,
> so their area can be defined.
that it applies to things which's definition can be used for line
segments. That doesn't mean that our concept of line segments admits
area. Something's been lost in the abstraction. Like, but not
necessarily homomorphic, with 'no is maybe and maybe is yes'.
Peter T. Daniels
Aug 18, 2012, 10:22:53 PM8/18/12
to
On Aug 18, 8:13 pm, António Marques <ento...@gmail.com> wrote:
> For me, if you say a 'line segment' has an area of 0, I'll consider
> that you're in fact talking about a closed polygon with at least one
> side of length 0. Otherwise, take a triangle and remove one of the
> sides. What does 'area' mean when applied to the remaining shape?-
> For me, if you say a 'line segment' has an area of 0, I'll consider
> that you're in fact talking about a closed polygon with at least one
> side of length 0. Otherwise, take a triangle and remove one of the
Its area would be infinite, because it's unbounded and so "leaks" out
into the entire universe?
Peter T. Daniels
Aug 18, 2012, 10:25:29 PM8/18/12
to
On Aug 18, 8:21 pm, António Marques <ento...@gmail.com> wrote:
> On Aug 19, 12:34 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > Mathematical lines have nothing to do with mass, temperature, color,
> > or loudness, but they can be sets of points in two or more dimensions,
> > so their area can be defined.
>
> I think what you're saying is that there is a way to define 'area' so
> that it applies to things which's definition can be used for line
shouldn't that be "that's"? Not only is there precedent, but it's a
> On Aug 19, 12:34 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
> > Mathematical lines have nothing to do with mass, temperature, color,
> > or loudness, but they can be sets of points in two or more dimensions,
> > so their area can be defined.
>
> I think what you're saying is that there is a way to define 'area' so
> that it applies to things which's definition can be used for line
restrictive relative!
Peter T. Daniels
Aug 18, 2012, 10:20:21 PM8/18/12
to
two dimensions?
How can things with one and zero dimensions be subsets of things with
two dimensions? They don't _have_ two dimensions!
Wait, is this gonna be one of those rhetorical tricks like
0.999999999... = 1?
Message has been deleted
pauljk
Aug 19, 2012, 1:40:09 AM8/19/12
to
"Guy Barry" <guy....@blueyonder.co.uk> wrote in message
news:X3IXr.905915$IP4.1...@fx26.am4...
> "pauljk" wrote in message news:k0ni75$p5o$3...@dont-email.me...
>
>> I was originally objecting to Guy's word "times" in his
Of course it's a made-up term, and it is a made-up objection.
> is a mystery to me, but you did say "square zillion". There's no analogy with
> "square metre", because "zillion" isn't a unit (if it has any meaning at all). So
> the only way I could interpret a "square zillion" would be as a "squared zillion",
> i.e. a zillion times a zillion.
>
> But this is getting zilly.
Smile, you are on candid camera!
pjk
news:X3IXr.905915$IP4.1...@fx26.am4...
> "pauljk" wrote in message news:k0ni75$p5o$3...@dont-email.me...
>
>> I was originally objecting to Guy's word "times" in his
>> "A zillion times a zillion."
>
> How you can object to anyone's interpretation of a completely made-up term
>
Of course it's a made-up term, and it is a made-up objection.
> is a mystery to me, but you did say "square zillion". There's no analogy with
> "square metre", because "zillion" isn't a unit (if it has any meaning at all). So
> the only way I could interpret a "square zillion" would be as a "squared zillion",
> i.e. a zillion times a zillion.
>
> But this is getting zilly.
Smile, you are on candid camera!
pjk
Paul {Hamilton Rooney}
Aug 19, 2012, 1:40:23 AM8/19/12
to
than my oranges. My plums are medium.
Of course you can compare the size of lines, areas and volumes.
The tiny lines I draw each month on the wall to mark my kids' height are
way smaller than the floor.
A square yard is way smaller than a cubic yard.
--
"THOSE WHO INDULGE IN CHEST-BEATING ABOUT HOW THEY ALWAYS WIN SEEM TO
OVERLOOK THE FACT THAT THE SO-CALLED SIG-ABUSERS ALWAYS WIN, TOO. USENET
IS LIKE THAT. IF SUCH MEANINGLESS LABELS ARE TO BE PRESSED INTO SERVICE,
THEN I WOULD SAY THAT PAUL HAS WON. NOT ONLY BY HIS UNDOUBTED STAMINA,
BUT BY THE SUSTAINED GRACE, CHARM, AND MISCHIEVOUS WIT OF HIS RESPONSES."
JAMES FOLLETT, NOVELIST (WRITING IN THE NEWSGROUP DEMON.LOCAL)
PAUL [HAMILTON ROONEY]
Paul {Hamilton Rooney}
Aug 19, 2012, 1:45:12 AM8/19/12
to
On 19-Aug-12 4:42 AM, Peter T. Daniels wrote:
. A cubic
> meter can just as easily be conceptualized as a sphere of a certain
> radius,
Not by most people, I would venture to suggest.
. A cubic
> meter can just as easily be conceptualized as a sphere of a certain
> radius,
But I don't conceptualize very much.
I'm quite good at imagining.
pauljk
Aug 19, 2012, 1:48:03 AM8/19/12
to
"Evan Kirshenbaum" <evan.kir...@gmail.com> wrote in message
news:4no0yz...@gmail.com...
> Jerry Friedman <jerry_f...@yahoo.com> writes:
>
>> On Aug 17, 3:32 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
>> wrote:
imply they are paid cubic dollars? :-)
pjk
Paul {Hamilton Rooney}
Aug 19, 2012, 1:48:46 AM8/19/12
to
On 18-Aug-12 11:02 PM, Paul Wolff wrote:
> In message <slrnk2t395....@mbp55.local>, Lewis
> <g.k...@gmail.com.dontsendmecopies> writes
>> In message <k0lg98$q9v$1...@dont-email.me>
>> pauljk <paul....@xtra.co.nz> wrote:
>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>
>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
Every house or apartment that I've lived in has had oblong meters.
Well, cuboid, really.
> In message <slrnk2t395....@mbp55.local>, Lewis
> <g.k...@gmail.com.dontsendmecopies> writes
>> In message <k0lg98$q9v$1...@dont-email.me>
>> pauljk <paul....@xtra.co.nz> wrote:
>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>
>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>>
>>>>> Isn't "squazillion" just a contraction of "square zillion", ie.
>>>>> measure
>>>>> of an area?
>>>>
>>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>> bigger than a
>>>> zillion then :-)
>>
>>> That's not what I said, read it again.
>>> Square X is just a different unit than X.
>>> For instance, one square metre is still only one metre, it's
>>> an area of one square metre, unlike plain metre which is
>>> a distance of one metre.
>>
>> A square meter is much larger than a meter. Infinitely so, in fact. A
>> cubic meter is much larger than a square meter too, and even larger than
>> a meter, but still infinitely larger than both.
>>
>>>>> Isn't "squazillion" just a contraction of "square zillion", ie.
>>>>> measure
>>>>> of an area?
>>>>
>>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>> bigger than a
>>>> zillion then :-)
>>
>>> That's not what I said, read it again.
>>> Square X is just a different unit than X.
>>> For instance, one square metre is still only one metre, it's
>>> an area of one square metre, unlike plain metre which is
>>> a distance of one metre.
>>
>> A square meter is much larger than a meter. Infinitely so, in fact. A
>> cubic meter is much larger than a square meter too, and even larger than
>> a meter, but still infinitely larger than both.
>>
> It's clear to me that a square meter is one meter times greater than a
> linear meter, and a cubic meter one meter times greater than a square
> meter.
I'd love to agree or disagree, but I've never seen any square meters.
> linear meter, and a cubic meter one meter times greater than a square
> meter.
Every house or apartment that I've lived in has had oblong meters.
Well, cuboid, really.
Paul {Hamilton Rooney}
Aug 19, 2012, 1:49:45 AM8/19/12
to
pauljk
Aug 19, 2012, 1:53:56 AM8/19/12
to
news:zk5sxk...@gmail.com...
pjk
P.S. Assuming that metre equals meter exactly.
I hope there's not some weird conversion ratio like gallon
to US gallon.
> Paul Wolff <boun...@two.wolff.co.uk> writes:
>
>> In message <slrnk2t395....@mbp55.local>, Lewis
>> <g.k...@gmail.com.dontsendmecopies> writes
>>>In message <k0lg98$q9v$1...@dont-email.me>
>>> pauljk <paul....@xtra.co.nz> wrote:
>>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>>
>>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>>>
>>>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>>>> of an area?
>>>>>
>>>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>>> bigger than a
>>>>> zillion then :-)
>>>
>>>> That's not what I said, read it again.
>>>> Square X is just a different unit than X.
>>>> For instance, one square metre is still only one metre, it's
>>>> an area of one square metre, unlike plain metre which is
>>>> a distance of one metre.
>>>
>>>A square meter is much larger than a meter. Infinitely so, in fact. A
>>>cubic meter is much larger than a square meter too, and even larger than
>>>a meter, but still infinitely larger than both.
>>>
>
>> In message <slrnk2t395....@mbp55.local>, Lewis
>> <g.k...@gmail.com.dontsendmecopies> writes
>>>In message <k0lg98$q9v$1...@dont-email.me>
>>> pauljk <paul....@xtra.co.nz> wrote:
>>>> "Guy Barry" <guy....@blueyonder.co.uk> wrote in message
>>>> news:b_kXr.687426$GO2.5...@fx05.am4...
>>>>>
>>>>> "pauljk" wrote in message news:k0kbhj$gli$1...@dont-email.me...
>>>>>
>>>>>> Isn't "squazillion" just a contraction of "square zillion", ie. measure
>>>>>> of an area?
>>>>>
>>>>> I hadn't thought of that! A zillion times a zillion. Definitely
>>>>> bigger than a
>>>>> zillion then :-)
>>>
>>>> That's not what I said, read it again.
>>>> Square X is just a different unit than X.
>>>> For instance, one square metre is still only one metre, it's
>>>> an area of one square metre, unlike plain metre which is
>>>> a distance of one metre.
>>>
>>>A square meter is much larger than a meter. Infinitely so, in fact. A
>>>cubic meter is much larger than a square meter too, and even larger than
>>>a meter, but still infinitely larger than both.
>>>
>> It's clear to me that a square meter is one meter times greater than a
>> linear meter, and a cubic meter one meter times greater than a square
>> meter.
>
> Now all you have to do is show that one meter is greater than one.
Oh, that's easy, it's metre times more than one.
>> linear meter, and a cubic meter one meter times greater than a square
>> meter.
>
> Now all you have to do is show that one meter is greater than one.
pjk
P.S. Assuming that metre equals meter exactly.
I hope there's not some weird conversion ratio like gallon
to US gallon.
Joachim Pense
Aug 19, 2012, 3:01:44 AM8/19/12
to
Am 19.08.2012 04:20, schrieb Peter T. Daniels:
> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>>
>>
>>
>>>> Okay. If you were, you could figure out why your objection above
>>>> isn't valid (along the lines of what Joachim Pense said).
>>
>>> No. A line segment is, by definition, a thing with one and only one
>>> dimension.
>>
>>> An area is, by definition, a property of things with two dimensions.
>>
>>> Therefore, a line segment cannot have an area (and it is thusT
> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>>
>>
>>
>>>> Okay. If you were, you could figure out why your objection above
>>>> isn't valid (along the lines of what Joachim Pense said).
>>
>>> No. A line segment is, by definition, a thing with one and only one
>>> dimension.
>>
>>> An area is, by definition, a property of things with two dimensions.
>>
>>> meaningless to assign any number at all to "the area of a line
>>> segment").
>>
>> An area is, by definition, a property of _subsets_ of spaces with two
>> dimensions (like planes). Lines and points are such subsets, having area
>> zero. A cube is not a subset of a two-dimensional space.
>
> An area is, by definition, a property of some subsets of spaces with
> two dimensions?
>
> How can things with one and zero dimensions be subsets of things with
> two dimensions? They don't _have_ two dimensions!
>
A plane is a set of points. A triangle in that plane is a subset of the
>>> segment").
>>
>> An area is, by definition, a property of _subsets_ of spaces with two
>> dimensions (like planes). Lines and points are such subsets, having area
>> zero. A cube is not a subset of a two-dimensional space.
>
> An area is, by definition, a property of some subsets of spaces with
> two dimensions?
>
> How can things with one and zero dimensions be subsets of things with
> two dimensions? They don't _have_ two dimensions!
>
plane. A line in that plane is another subset of the plane. 1000
arbitrary isolated points are yet another subset of the plane.
Joachim
Joachim Pense
Aug 19, 2012, 3:08:04 AM8/19/12
to
Am 18.08.2012 17:52, schrieb Evan Kirshenbaum:
>
> "A cubic meter is much larger than a square meter too, and even larger
>
> "A cubic meter is much larger than a square meter too, and even larger
> than a meter". If that's not "larger" in the sense of "has more
> volume", then in what sense is it?
>
A triangle of area a square meter as just as much volume as a line of
> volume", then in what sense is it?
>
length a meter: both have volume zero.
This is obviously not what they mean when they say that one is larger
than the other.
Joachim
Paul {Hamilton Rooney}
Aug 19, 2012, 3:11:08 AM8/19/12
to
Points have no area. A million points have no area.
We're talking apples and cuttlefish here, if you'll pardon the phrase.
Paul {Hamilton Rooney}
Aug 19, 2012, 3:19:13 AM8/19/12
to
Lines are smaller than areas and areas are smaller than volumes, for any
unit.
Just ask teh wife: she's usually right.
R H Draney
Aug 19, 2012, 4:05:36 AM8/19/12
to
GordonD filted:
>
>"R H Draney" <dado...@spamcop.net> wrote in message
>
>"R H Draney" <dado...@spamcop.net> wrote in message
>news:k0nl9...@drn.newsguy.com...
>> Guy Barry filted:
>>>
>>>More seriously, has anyone ever commented on the irregular formation of
>>>words like "billion", "trillion" and so on? They appear to contain the
>>>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
>>>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
>>>indicates an enlargement or augmentation.
>>
>> Another instance of "-orama syndrome" (also known as "the -teria
>> principle")....r
>
>
>Is that anything like adding "-gate" to a noun to describe a scandal of some
>sort (after Watergate, even though that was the name of the hotel and had
>nothing to do with water), or "-holic" to indicate that you are very fond of
>something (usually seen as chocoholic)?
Welcome to the Suffix-palooza Morpheme-thon 2012!...r
>> Guy Barry filted:
>>>
>>>More seriously, has anyone ever commented on the irregular formation of
>>>words like "billion", "trillion" and so on? They appear to contain the
>>>prefix "bi-", "tri-" and so on, but "-llion" has no meaning on its own.
>>>"Million" comes from Latin "mille" (a thousand) plus "-ion", which I think
>>>indicates an enlargement or augmentation.
>>
>> Another instance of "-orama syndrome" (also known as "the -teria
>> principle")....r
>
>
>Is that anything like adding "-gate" to a noun to describe a scandal of some
>sort (after Watergate, even though that was the name of the hotel and had
>nothing to do with water), or "-holic" to indicate that you are very fond of
>something (usually seen as chocoholic)?
R H Draney
Aug 19, 2012, 4:14:26 AM8/19/12
to
Paul {Hamilton Rooney} filted:
>
>On 18-Aug-12 11:02 PM, Paul Wolff wrote:
>> It's clear to me that a square meter is one meter times greater than a
>> linear meter, and a cubic meter one meter times greater than a square
>> meter.
>
>I'd love to agree or disagree, but I've never seen any square meters.
>Every house or apartment that I've lived in has had oblong meters.
>Well, cuboid, really.
If I had to put a name to the shape of mine, I'd call it cylindrical....r
>On 18-Aug-12 11:02 PM, Paul Wolff wrote:
>> It's clear to me that a square meter is one meter times greater than a
>> linear meter, and a cubic meter one meter times greater than a square
>> meter.
>
>I'd love to agree or disagree, but I've never seen any square meters.
>Every house or apartment that I've lived in has had oblong meters.
>Well, cuboid, really.
Ian Noble
Aug 19, 2012, 4:34:32 AM8/19/12
to
On Sat, 18 Aug 2012 16:24:21 +0000 (UTC), Lewis
<g.k...@gmail.com.dontsendmecopies> wrote:
>In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
It's the difference between having a bank balance of zero and having
no bank account.
Cheers - Ian
(BrE: Yorks., Hants.)
<g.k...@gmail.com.dontsendmecopies> wrote:
>In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
> Peter T. Daniels <gram...@verizon.net> wrote:
>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
>>> Surely the area of a 1-meter line segment is 0, so it's not
>>> incommensurate with the area of a square 1 meter on a side.
>
>> Surely there's a difference between a dimension of 0 and complete
>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>> doesn't have an area of 0.
>
>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>
>>> Surely the area of a 1-meter line segment is 0, so it's not
>>> incommensurate with the area of a square 1 meter on a side.
>
>> Surely there's a difference between a dimension of 0 and complete
>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>> doesn't have an area of 0.
>
>How is 0 mass different from no mass? 0 means none. 0 length is no
>length, and zero area is no area.
Put another way:
>length, and zero area is no area.
It's the difference between having a bank balance of zero and having
no bank account.
Cheers - Ian
(BrE: Yorks., Hants.)
Guy Barry
Aug 19, 2012, 4:38:34 AM8/19/12
to
"R H Draney" wrote in message news:k0q6o...@drn.newsguy.com...
> GordonD filted:
> > Is that anything like adding "-gate" to a noun to describe a scandal of
> > some
> > sort (after Watergate, even though that was the name of the hotel and
> > had
> > nothing to do with water), or "-holic" to indicate that you are very
> > fond of
> >something (usually seen as chocoholic)?
> Welcome to the Suffix-palooza Morpheme-thon 2012!...r
it might be "reanalysis", but that appears to be slightly different.)
--
Guy Barry
Guy Barry
Aug 19, 2012, 4:43:47 AM8/19/12
to
"Ian Noble" wrote in message
news:l09138ltgst4kup9q...@4ax.com...
"Water has no freezing point" would mean that it never froze.
Or, even better, Paul Erdős has an Erdős number of zero, whereas I have no
Erdős number (as far as I know).
--
Guy Barry
Ian Noble
Aug 19, 2012, 4:47:57 AM8/19/12
to
On Sat, 18 Aug 2012 11:31:18 -0700, Evan Kirshenbaum
<evan.kir...@gmail.com> wrote:
>Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>> In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
>> Peter T. Daniels <gram...@verizon.net> wrote:
>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>> Surely there's a difference between a dimension of 0 and complete
>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>> doesn't have an area of 0.
>>
>different. Does a line have a mass of zero? A temperature of zero?
>What's it's color? How loud is it?
It doesn't have area. Area requires a second dimension - and a line
doesn't have that, any more than (as you recognise) it has temperature
or volume.
(It might be convenient, in some contexts, to simplify things by
*saying* that it has an area of zero - theoretical physicists seem to
do that sort of thing all the time - but it has to be done with
caution. If you lose track of your simplification, you can end up
doing any number of invalid things in your logic, and ending up at all
sorts of stupid conclusions. A simple example would be the "One cow
has 4 more legs than no cow; no cow has 13 legs; therefore every cow
has 17 legs" sort of argument.)
Cheers - Ian
<evan.kir...@gmail.com> wrote:
>Lewis <g.k...@gmail.com.dontsendmecopies> writes:
>
>> In message <73180ee6-f2f2-4a9d...@z6g2000vbc.googlegroups.com>
>> Peter T. Daniels <gram...@verizon.net> wrote:
>>> On Aug 17, 10:29 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>>
>>>> Surely the area of a 1-meter line segment is 0, so it's not
>>>> incommensurate with the area of a square 1 meter on a side.
>>
>>> Surely there's a difference between a dimension of 0 and complete
>>> nonexistence -- a 1-meter line segment has no area, so a fortiori it
>>> doesn't have an area of 0.
>>
>> How is 0 mass different from no mass? 0 means none. 0 length is no
>> length, and zero area is no area.
>
>> length, and zero area is no area.
>
>I can't decide whether or not I think that a line doesn't have area or
>whether it has area zero, but I agree with Peter that they're
>different. Does a line have a mass of zero? A temperature of zero?
>What's it's color? How loud is it?
It doesn't have area. Area requires a second dimension - and a line
doesn't have that, any more than (as you recognise) it has temperature
or volume.
(It might be convenient, in some contexts, to simplify things by
*saying* that it has an area of zero - theoretical physicists seem to
do that sort of thing all the time - but it has to be done with
caution. If you lose track of your simplification, you can end up
doing any number of invalid things in your logic, and ending up at all
sorts of stupid conclusions. A simple example would be the "One cow
has 4 more legs than no cow; no cow has 13 legs; therefore every cow
has 17 legs" sort of argument.)
Cheers - Ian
J. J. Lodder
Aug 19, 2012, 5:50:04 AM8/19/12
to
Paul {Hamilton Rooney} <paulv...@snotmail.com> wrote:
> On 19-Aug-12 3:20 AM, Joachim Pense wrote:
> >
> >
> > Am 18.08.2012 20:34, schrieb Evan Kirshenbaum:
> >
> >>
> >> Taking that approach, a meter has volume zero, too, so in what sense
> >> is one square meter "even larger" in the second comparison than in the
> >> first? That's what I was objecting to.
> >>
> >
> > It isn't.
> >
> > Joachim
>
>
>
> Comparing apples and oranges, yes. But my apples are definitely bigger
> than my oranges. My plums are medium.
> Of course you can compare the size of lines, areas and volumes.
>
> The tiny lines I draw each month on the wall to mark my kids' height are
> way smaller than the floor.
>
> A square yard is way smaller than a cubic yard.
Considered as a subset of a higher dimensional space
> On 19-Aug-12 3:20 AM, Joachim Pense wrote:
> >
> >
> > Am 18.08.2012 20:34, schrieb Evan Kirshenbaum:
> >
> >>
> >> Taking that approach, a meter has volume zero, too, so in what sense
> >> is one square meter "even larger" in the second comparison than in the
> >> first? That's what I was objecting to.
> >>
> >
> > It isn't.
> >
> > Joachim
>
>
>
> Comparing apples and oranges, yes. But my apples are definitely bigger
> than my oranges. My plums are medium.
> Of course you can compare the size of lines, areas and volumes.
>
> The tiny lines I draw each month on the wall to mark my kids' height are
> way smaller than the floor.
>
> A square yard is way smaller than a cubic yard.
every point set in any space has (hyper)volume zero.
No doubt this observation is a great step forward in our understanding.
(like the Bellman's blank map for geography)
Jan
CDB
Aug 19, 2012, 6:43:00 AM8/19/12
to
On 19/08/2012 4:38 AM, Guy Barry wrote:
> "R H Draney" wrote:
>> GordonD filted:
[holicgateorama]
>> Welcome to the Suffix-palooza Morpheme-thon 2012!...r
> Is there a generally accepted term for this phenomenon? (At first I
> thought it might be "reanalysis", but that appears to be slightly
> different.)
Wordburger.
> "R H Draney" wrote:
>> GordonD filted:
[holicgateorama]
>> Welcome to the Suffix-palooza Morpheme-thon 2012!...r
> Is there a generally accepted term for this phenomenon? (At first I
> thought it might be "reanalysis", but that appears to be slightly
> different.)
Paul {Hamilton Rooney}
Aug 19, 2012, 8:19:05 AM8/19/12
to
Paul {Hamilton Rooney}
Aug 19, 2012, 8:21:28 AM8/19/12
to
Jerry Friedman
Aug 19, 2012, 9:15:25 AM8/19/12
to
Erdös, then that person’s Erdös number is said to be infinite."
http://www.oakland.edu/enp/readme/
--
Jerry Friedman's Erdös number is 5 (or less).
Peter T. Daniels
Aug 19, 2012, 9:32:02 AM8/19/12
to
On Aug 19, 3:11 am, Paul {Hamilton Rooney} <paulvloo...@snotmail.com>
wrote:
it's a subset of a plane!
Who says a plane is a set of points?
wrote:
> On 19-Aug-12 3:01 PM, Joachim Pense wrote:
> > Am 19.08.2012 04:20, schrieb Peter T. Daniels:
> >> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
> >>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>
> >>>> No. A line segment is, by definition, a thing with one and only one
> >>>> dimension.
>
> >>>> An area is, by definition, a property of things with two dimensions.
>
> >>>> Therefore, a line segment cannot have an area (and it is thus
> > Am 19.08.2012 04:20, schrieb Peter T. Daniels:
> >> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
> >>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>
> >>>> No. A line segment is, by definition, a thing with one and only one
> >>>> dimension.
>
> >>>> An area is, by definition, a property of things with two dimensions.
>
> >>>> Therefore, a line segment cannot have an area (and it is thus
> >>>> meaningless to assign any number at all to "the area of a line
> >>>> segment").
>
> >>> An area is, by definition, a property of _subsets_ of spaces with two
> >>> dimensions (like planes). Lines and points are such subsets, having area
> >>> zero. A cube is not a subset of a two-dimensional space.
>
> >> An area is, by definition, a property of some subsets of spaces with
> >> two dimensions?
>
> >> How can things with one and zero dimensions be subsets of things with
> >> two dimensions? They don't _have_ two dimensions!
>
> > A plane is a set of points. A triangle in that plane is a subset of the
> > plane. A line in that plane is another subset of the plane. 1000
> > arbitrary isolated points are yet another subset of the plane.
>
> >>>> segment").
>
> >>> An area is, by definition, a property of _subsets_ of spaces with two
> >>> dimensions (like planes). Lines and points are such subsets, having area
> >>> zero. A cube is not a subset of a two-dimensional space.
>
> >> An area is, by definition, a property of some subsets of spaces with
> >> two dimensions?
>
> >> How can things with one and zero dimensions be subsets of things with
> >> two dimensions? They don't _have_ two dimensions!
>
> > A plane is a set of points. A triangle in that plane is a subset of the
> > plane. A line in that plane is another subset of the plane. 1000
> > arbitrary isolated points are yet another subset of the plane.
>
> No it isn't.
> Points have no area. A million points have no area.
> We're talking apples and cuttlefish here, if you'll pardon the phrase.
Joachim seems to be saying that a _single point_ has an area because
> Points have no area. A million points have no area.
> We're talking apples and cuttlefish here, if you'll pardon the phrase.
it's a subset of a plane!
Who says a plane is a set of points?
Peter T. Daniels
Aug 19, 2012, 9:34:04 AM8/19/12
to
but no one can have either no Edos number or an Erdos number of
infinity.
Joachim Pense
Aug 19, 2012, 9:52:58 AM8/19/12
to
Joachim
Jerry Friedman
Aug 19, 2012, 9:54:32 AM8/19/12
to
On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
...
> > > Hmm, is there more than one empty set? Is the set of all unicorns the
> > > same as the set of all living people 150 years old?
>
> > In mathematics there's only one empty set. (I don't know whether
> > there might be some non-standard approach or non-mathematical approach
> > with different empty sets.)
>
> In computer programming, there sure are different empty sets; an array
> of type X is not generally replaceable with an array of type Y, even
> if both are empty.
I'd call those empty arrays. If programmers call them empty sets,
then I'd say there's only one empty set in the sense of set theory.
> And you can add elements to an empty set or values to a numeric object
> of value 0, whereas you can't do anything with a null set or a null
> number. The point here is that even if you dismiss these as artefacts
> of notation or memory management, they do serve purposes. For
> instance, you can have a function the purpose of which is to determine
> the position of the first occurrence of a character in a string. If
> the character isn't part of the string, it's not correct to reply '0'.
> The usual solution to problems like these has been to reply '-1',
> which will sort of worjk as long as all the valid replies are
> positive; however, the elegant and meaningful reply would be 'null'.
> And boolean values? True is 'yes', false is 'no'. What is null? The
> correct thing to consider is that it means 'undetermined'.
Fine, but that's not the empty set in the sense of set theory.
> For me, if you say a 'line segment' has an area of 0, I'll consider
> that you're in fact talking about a closed polygon with at least one
> side of length 0.
I'm talking about a set of points in two or more dimensions. It
doesn't have to be bounded--for instance, the area of the points (x,
y) with x > 0 and 0 < y < e^(-x), which is the area under the curve of
y = e^(-x) from zero to infinity, is well defined (and equal to 1).
> Otherwise, take a triangle and remove one of the
> sides. What does 'area' mean when applied to the remaining shape?
We've got three points in a plane, A, B, and C. The area of the set
of points bounded by the line segments AB, BC, and CA--a triangle--is
given by our choice of well-known formulas [•]. By "remove one side",
I take it you mean "the set of points bounded by the line segments AB
and BC". This expression is meaningless; there is no such set of
points. So indeed, "area" doesn't mean anything when applied to it.
(On the other hand, the area of the three line segments, that is, the
sides of the triangle without the interior, is 0, and if you remove
one of them, it's still 0.)
[From another post]
> I think what you're saying is that there is a way to define 'area' so
> that it applies to things which's
Heh.
> definition can be used for line segments.
As long as it's clear that "you" includes all mathematicians, except
possibly for a set of measure 0 :-) For instance, see page 5 at
http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf
for the idea that points have 0 length and "boxes" can have 0 volume.
(That includes line segments with 0 area, volume, etc.)
This is also stated at Wikipedia, which I generally trust on math, and
at Mathworld, where it's not quite so explicit as it is in Terence
Tao's book.
> That doesn't mean that our concept of line segments admits
> area.
Mine does. Intuitively, as you make a rectangle thinner, it
approaches a line segment, and its area approaches 0.
Here's another appeal to intuition. It's part of our intuitive idea
of measure that if A and B and disjoint (non-intersecting) sets, the
measure of the union of A and B equals the measure of A + the measure
of B, right?
Consider two subsets of the real-number line: A = [0, 1) (the numbers
from 0 to 1 including 0 but not 1), and B = {1}. The union of those
sets is C= [0, 1] (the numbers from 0 to to 1 including both 0 and
1). Both A and C have length 1. It works perfectly to say that the
length of C = the length of A plus the length of B, as 1 = 1 + 0. To
say that the length of B is undefined and we can't use the equation is
to make a simple and perfectly workable thing complicated and
unworkable.
(Apologies to those who didn't need the definitions of the intervals,
etc. Some here may have wanted them.)
> Something's been lost in the abstraction. Like, but not
> necessarily homomorphic, with 'no is maybe and maybe is yes'.
I have no idea what part of measure theory your "no is maybe" phrase
is supposed to connect to. Of all the things to accuse of lacking
rigor and self-consistency! Or am I misunderstanding you.
[*] "Well-known" doesn't necessarily mean I remember them, other than
A = bh/2.
--
Jerry Friedman
> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
...
> > > Hmm, is there more than one empty set? Is the set of all unicorns the
> > > same as the set of all living people 150 years old?
>
> > In mathematics there's only one empty set. (I don't know whether
> > there might be some non-standard approach or non-mathematical approach
> > with different empty sets.)
>
> In computer programming, there sure are different empty sets; an array
> of type X is not generally replaceable with an array of type Y, even
> if both are empty.
I'd call those empty arrays. If programmers call them empty sets,
then I'd say there's only one empty set in the sense of set theory.
> And you can add elements to an empty set or values to a numeric object
> of value 0, whereas you can't do anything with a null set or a null
> number. The point here is that even if you dismiss these as artefacts
> of notation or memory management, they do serve purposes. For
> instance, you can have a function the purpose of which is to determine
> the position of the first occurrence of a character in a string. If
> the character isn't part of the string, it's not correct to reply '0'.
> The usual solution to problems like these has been to reply '-1',
> which will sort of worjk as long as all the valid replies are
> positive; however, the elegant and meaningful reply would be 'null'.
> And boolean values? True is 'yes', false is 'no'. What is null? The
> correct thing to consider is that it means 'undetermined'.
Fine, but that's not the empty set in the sense of set theory.
> For me, if you say a 'line segment' has an area of 0, I'll consider
> that you're in fact talking about a closed polygon with at least one
> side of length 0.
I'm talking about a set of points in two or more dimensions. It
doesn't have to be bounded--for instance, the area of the points (x,
y) with x > 0 and 0 < y < e^(-x), which is the area under the curve of
y = e^(-x) from zero to infinity, is well defined (and equal to 1).
> Otherwise, take a triangle and remove one of the
> sides. What does 'area' mean when applied to the remaining shape?
We've got three points in a plane, A, B, and C. The area of the set
of points bounded by the line segments AB, BC, and CA--a triangle--is
given by our choice of well-known formulas [•]. By "remove one side",
I take it you mean "the set of points bounded by the line segments AB
and BC". This expression is meaningless; there is no such set of
points. So indeed, "area" doesn't mean anything when applied to it.
(On the other hand, the area of the three line segments, that is, the
sides of the triangle without the interior, is 0, and if you remove
one of them, it's still 0.)
[From another post]
> I think what you're saying is that there is a way to define 'area' so
> that it applies to things which's
Heh.
> definition can be used for line segments.
As long as it's clear that "you" includes all mathematicians, except
possibly for a set of measure 0 :-) For instance, see page 5 at
http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf
for the idea that points have 0 length and "boxes" can have 0 volume.
(That includes line segments with 0 area, volume, etc.)
This is also stated at Wikipedia, which I generally trust on math, and
at Mathworld, where it's not quite so explicit as it is in Terence
Tao's book.
> That doesn't mean that our concept of line segments admits
> area.
Mine does. Intuitively, as you make a rectangle thinner, it
approaches a line segment, and its area approaches 0.
Here's another appeal to intuition. It's part of our intuitive idea
of measure that if A and B and disjoint (non-intersecting) sets, the
measure of the union of A and B equals the measure of A + the measure
of B, right?
Consider two subsets of the real-number line: A = [0, 1) (the numbers
from 0 to 1 including 0 but not 1), and B = {1}. The union of those
sets is C= [0, 1] (the numbers from 0 to to 1 including both 0 and
1). Both A and C have length 1. It works perfectly to say that the
length of C = the length of A plus the length of B, as 1 = 1 + 0. To
say that the length of B is undefined and we can't use the equation is
to make a simple and perfectly workable thing complicated and
unworkable.
(Apologies to those who didn't need the definitions of the intervals,
etc. Some here may have wanted them.)
> Something's been lost in the abstraction. Like, but not
> necessarily homomorphic, with 'no is maybe and maybe is yes'.
I have no idea what part of measure theory your "no is maybe" phrase
is supposed to connect to. Of all the things to accuse of lacking
rigor and self-consistency! Or am I misunderstanding you.
[*] "Well-known" doesn't necessarily mean I remember them, other than
A = bh/2.
--
Jerry Friedman
pauljk
Aug 19, 2012, 10:40:11 AM8/19/12
to
"Joachim Pense" <sn...@pense-mainz.eu> wrote in message
news:a9c9dq...@mid.individual.net...
Right, there should be no problem with that.
The plane being a set of zero sized points has a non-zero sized area.
This, of course, is achieved by the virtue of having infinite number
of points in the set.
In fact, all non-zero sized subsets of the plane have infinite number
of points in them.
pjk
news:a9c9dq...@mid.individual.net...
The plane being a set of zero sized points has a non-zero sized area.
This, of course, is achieved by the virtue of having infinite number
of points in the set.
In fact, all non-zero sized subsets of the plane have infinite number
of points in them.
pjk
GordonD
Aug 19, 2012, 11:17:07 AM8/19/12
to
"Peter T. Daniels" <gram...@verizon.net> wrote in message
news:ec3e02be-de65-4fd5...@d7g2000vbv.googlegroups.com...
On Aug 18, 12:26 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> On Aug 18, 9:52 am, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> wrote:
> > >> >>news:b_kXr.687426$GO2.5...@fx05.am4...
>
> > >> >>> "pauljk" wrote in messagenews:k0kbhj$gli$1...@dont-email.me...
> than a square meter, which only has area, and even more larger [*]
> than a meter, which only has length."
>
> This doesn't make mathematical sense if you're talking about volume,
> since as you say, both the square meter and the linear meter have a
> volume of 0. It comes closer to making sense if you're talking about
> area and think of the cube as having infinite area. I don't think
> mathematicians think of cubical volumes as having area, though.
>
> (In another sense, you could say the cube has an area of 6 m^2.)
Nowhere has a cube been specified as the object of discussion. A cubic
there somewhere, and a 4/3, IIRC from 10th-grade geometry.)
---------------
Volume of a sphere is 4/3 x pi x radius cubed
Surface area is 4 x pi x radius squared (though I had to look that one up).
So given the direction of this thread, does that make a sphere four times
the size of a circle?
--
Gordon Davie
Edinburgh, Scotland
"Slipped the surly bonds of Earth...to touch the face of God."
news:ec3e02be-de65-4fd5...@d7g2000vbv.googlegroups.com...
On Aug 18, 12:26 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> On Aug 18, 9:52 am, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> wrote:
>
>
>
>
>
> > Jerry Friedman <jerry_fried...@yahoo.com> writes:
> > > On Aug 17, 3:32 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> > > wrote:
> > >> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
> > >> > In message <k0lg98$q9...@dont-email.me>
> > >> > pauljk <paul.kr...@xtra.co.nz> wrote:
> > >> >> "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote in message
>
>
>
>
> > Jerry Friedman <jerry_fried...@yahoo.com> writes:
> > > On Aug 17, 3:32 pm, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
> > > wrote:
> > >> Lewis <g.kr...@gmail.com.dontsendmecopies> writes:
> > >> > In message <k0lg98$q9...@dont-email.me>
> > >> > pauljk <paul.kr...@xtra.co.nz> wrote:
> > >> >>news:b_kXr.687426$GO2.5...@fx05.am4...
>
> > >> >>> "pauljk" wrote in messagenews:k0kbhj$gli$1...@dont-email.me...
>
> > >> >>>> Isn't "squazillion" just a contraction of "square zillion", ie.
> > >> >>>> measure
> > >> >>>> of an area?
>
> > >> >>> I hadn't thought of that! A zillion times a zillion. Definitely
> > >> >>> bigger than a
> > >> >>> zillion then :-)
>
> > >> >> That's not what I said, read it again.
> > >> >> Square X is just a different unit than X.
> > >> >> For instance, one square metre is still only one metre, it's
> > >> >> an area of one square metre, unlike plain metre which is
> > >> >> a distance of one metre.
>
> > >> > A square meter is much larger than a meter. Infinitely so, in fact.
> > >> >>>> Isn't "squazillion" just a contraction of "square zillion", ie.
> > >> >>>> measure
> > >> >>>> of an area?
>
> > >> >>> I hadn't thought of that! A zillion times a zillion. Definitely
> > >> >>> bigger than a
> > >> >>> zillion then :-)
>
> > >> >> That's not what I said, read it again.
> > >> >> Square X is just a different unit than X.
> > >> >> For instance, one square metre is still only one metre, it's
> > >> >> an area of one square metre, unlike plain metre which is
> > >> >> a distance of one metre.
>
> > >> > A square meter is much larger than a meter. Infinitely so, in fact.
> > >> > A
> > >> > cubic meter is much larger than a square meter too, and even larger
> > >> > than
> > >> > cubic meter is much larger than a square meter too, and even larger
> > >> > than
> > >> > a meter, but still infinitely larger than both.
>
>
> > > Paging Paul "Curlytop" Townsend.
>
> > >> How would you go about showing that a square meter had more volume
> > >> than a meter?
>
> > > I don't see where anybody said it did.
>
>
> > >> How would you go about showing that a square meter had more volume
> > >> than a meter?
>
> > > I don't see where anybody said it did.
>
> > "A cubic meter is much larger than a square meter too, and even larger
> > than a meter". If that's not "larger" in the sense of "has more
> > volume", then in what sense is it?
>
> I took it to be, "A cubic meter has volume, which makes it much larger
> > than a meter". If that's not "larger" in the sense of "has more
> > volume", then in what sense is it?
>
> than a square meter, which only has area, and even more larger [*]
> than a meter, which only has length."
>
> This doesn't make mathematical sense if you're talking about volume,
> since as you say, both the square meter and the linear meter have a
> volume of 0. It comes closer to making sense if you're talking about
> area and think of the cube as having infinite area. I don't think
> mathematicians think of cubical volumes as having area, though.
>
> (In another sense, you could say the cube has an area of 6 m^2.)
Nowhere has a cube been specified as the object of discussion. A cubic
meter can just as easily be conceptualized as a sphere of a certain
radius, and its surface area is presumably not 6 m^2. (There's a pi in
there somewhere, and a 4/3, IIRC from 10th-grade geometry.)
---------------
Volume of a sphere is 4/3 x pi x radius cubed
Surface area is 4 x pi x radius squared (though I had to look that one up).
So given the direction of this thread, does that make a sphere four times
the size of a circle?
--
Gordon Davie
Edinburgh, Scotland
"Slipped the surly bonds of Earth...to touch the face of God."
Guy Barry
Aug 19, 2012, 11:34:16 AM8/19/12
to
"Peter T. Daniels" wrote in message
news:ca4aef54-c83c-414f...@cf4g2000vbb.googlegroups.com...
Erdos number (though I've no idea what it might be).
The vast majority of people have not published academic papers, hence they
have no Erdos number.
--
Guy Barry
Evan Kirshenbaum
Aug 19, 2012, 11:52:19 AM8/19/12
to
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |I like giving talks to industry,
SF Bay Area (1982-) |because one of the things that I've
Chicago (1964-1982) |found is that you really can't
|learn anything at the Harvard
evan.kir...@gmail.com |Business School.
| Clayton Christensen
http://www.kirshenbaum.net/ | Harvard Business School
Evan Kirshenbaum
Aug 19, 2012, 12:29:57 PM8/19/12
to
Jerry Friedman <jerry_f...@yahoo.com> writes:
> On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
>> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> ...
>
>> > > Hmm, is there more than one empty set? Is the set of all
>> > > unicorns the same as the set of all living people 150 years
>> > > old?
>>
>> > In mathematics there's only one empty set. (I don't know whether
>> > there might be some non-standard approach or non-mathematical approach
>> > with different empty sets.)
>>
>> In computer programming, there sure are different empty sets; an array
>> of type X is not generally replaceable with an array of type Y, even
>> if both are empty.
>
> I'd call those empty arrays. If programmers call them empty sets,
I wouldn't, but we also have sets, which can be empty.
> On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
>> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
>> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> ...
>
>> > > Hmm, is there more than one empty set? Is the set of all
>> > > unicorns the same as the set of all living people 150 years
>> > > old?
>>
>> > In mathematics there's only one empty set. (I don't know whether
>> > there might be some non-standard approach or non-mathematical approach
>> > with different empty sets.)
>>
>> In computer programming, there sure are different empty sets; an array
>> of type X is not generally replaceable with an array of type Y, even
>> if both are empty.
>
> I'd call those empty arrays. If programmers call them empty sets,
> then I'd say there's only one empty set in the sense of set theory.
mathematicians, like computer scientists, had formalisms for talking
about sets of objects of particular types. Having only a single empty
set means that if you take the intersection of say, two sets of
trancendental numbers, the result may be a set of integers (or a set
of avocados).
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |Oh, forget it: I can't write about
SF Bay Area (1982-) |this anymore until I find a much
Chicago (1964-1982) |more sarcastic typeface.
| Bill Bickel
evan.kir...@gmail.com
http://www.kirshenbaum.net/
Evan Kirshenbaum
Aug 19, 2012, 12:42:32 PM8/19/12
to
reanalysis.
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |If I may digress momentarily from
SF Bay Area (1982-) |the mainstream of this evening's
Chicago (1964-1982) |symposium, I'd like to sing a song
|which is completely pointless.
evan.kir...@gmail.com | Tom Lehrer
http://www.kirshenbaum.net/
Guy Barry
Aug 19, 2012, 12:43:27 PM8/19/12
to
"Evan Kirshenbaum" wrote in message news:haryx2...@gmail.com...
> My set theory is more than a bit rusty, but I thought that
> mathematicians, like computer scientists, had formalisms for talking
> about sets of objects of particular types.
is the unique set having no elements; its size or cardinality (count of
elements in a set) is zero."
Set theory isn't typed. You can have a set whose members are 1 and my
grandmother. (Probably not much use, but the set is well-defined.)
--
Guy Barry
Evan Kirshenbaum
Aug 19, 2012, 1:01:01 PM8/19/12
to
of having no Erdos number.
My Erdos number would appear to be either 4 or 5, depending on whether
patents count. (several, Bob Tarjan, Bin Zhang, George Forman).
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |"The Dynamics of Interbeing and
SF Bay Area (1982-) |Monological Imperatives in 'Dick
Chicago (1964-1982) |and Jane' : A Study in Psychic
|Transrelational Modes."
evan.kir...@gmail.com | Calvin
http://www.kirshenbaum.net/
Jerry Friedman
Aug 19, 2012, 1:00:08 PM8/19/12
to
On Aug 19, 10:29 am, Evan Kirshenbaum <evan.kirshenb...@gmail.com>
wrote:
may equal the set of avocados that ripened in both 2012 and 1812--but
that's the empty set, so it's not a set of either transcendental
numbers or avocados.
The first axiom of Zermelo-Fraenkel set theory is "Axiom of
Extensionality: If X and Y have the same elements, then X = Y."
http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
My impression is that any other formulation of set theory is pretty
non-standard.
--
Jerry Friedman
wrote:
> Jerry Friedman <jerry_fried...@yahoo.com> writes:
> > On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
> >> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> >> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> > ...
>
> >> > > Hmm, is there more than one empty set? Is the set of all
> >> > > unicorns the same as the set of all living people 150 years
> >> > > old?
>
> >> > In mathematics there's only one empty set. (I don't know whether
> >> > there might be some non-standard approach or non-mathematical approach
> >> > with different empty sets.)
>
> >> In computer programming, there sure are different empty sets; an array
> >> of type X is not generally replaceable with an array of type Y, even
> >> if both are empty.
>
> > I'd call those empty arrays. If programmers call them empty sets,
>
> I wouldn't, but we also have sets, which can be empty.
>
> > then I'd say there's only one empty set in the sense of set theory.
>
> My set theory is more than a bit rusty, but I thought that
> mathematicians, like computer scientists, had formalisms for talking
> about sets of objects of particular types. Having only a single empty
> set means that if you take the intersection of say, two sets of
> trancendental numbers, the result may be a set of integers (or a set
> of avocados).
I'd say that the intersection of two sets of transcendental numbers
> > On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
> >> On Aug 18, 5:48 pm, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> >> > On Aug 18, 9:30 am, "Peter T. Daniels" <gramma...@verizon.net> wrote:
> > ...
>
> >> > > Hmm, is there more than one empty set? Is the set of all
> >> > > unicorns the same as the set of all living people 150 years
> >> > > old?
>
> >> > In mathematics there's only one empty set. (I don't know whether
> >> > there might be some non-standard approach or non-mathematical approach
> >> > with different empty sets.)
>
> >> In computer programming, there sure are different empty sets; an array
> >> of type X is not generally replaceable with an array of type Y, even
> >> if both are empty.
>
> > I'd call those empty arrays. If programmers call them empty sets,
>
> I wouldn't, but we also have sets, which can be empty.
>
> > then I'd say there's only one empty set in the sense of set theory.
>
> My set theory is more than a bit rusty, but I thought that
> mathematicians, like computer scientists, had formalisms for talking
> about sets of objects of particular types. Having only a single empty
> set means that if you take the intersection of say, two sets of
> trancendental numbers, the result may be a set of integers (or a set
> of avocados).
may equal the set of avocados that ripened in both 2012 and 1812--but
that's the empty set, so it's not a set of either transcendental
numbers or avocados.
The first axiom of Zermelo-Fraenkel set theory is "Axiom of
Extensionality: If X and Y have the same elements, then X = Y."
http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
My impression is that any other formulation of set theory is pretty
non-standard.
--
Jerry Friedman
Peter T. Daniels
Aug 19, 2012, 1:22:18 PM8/19/12
to
On Aug 19, 10:40 am, "pauljk" <paul.kr...@xtra.co.nz> wrote:
> "Joachim Pense" <s...@pense-mainz.eu> wrote in message
Zero times infinity is still zero, so you can't attribute a plane's
area to its infinite number of points EVEN IF you think points do have
an area of 0 (which they don't; points have no area and so have no
area size, either).
> "Joachim Pense" <s...@pense-mainz.eu> wrote in message
area to its infinite number of points EVEN IF you think points do have
an area of 0 (which they don't; points have no area and so have no
area size, either).
Peter T. Daniels
Aug 19, 2012, 1:25:59 PM8/19/12
to
On Aug 19, 12:43 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> "Evan Kirshenbaum" wrote in messagenews:haryx2...@gmail.com...
You probably have had two grandmothers.
> "Evan Kirshenbaum" wrote in messagenews:haryx2...@gmail.com...
Peter T. Daniels
Aug 19, 2012, 1:30:20 PM8/19/12
to
On Aug 19, 11:17 am, "GordonD" <g.da...@btinternet.com> wrote:
> "Peter T. Daniels" <gramma...@verizon.net> wrote in messagenews:ec3e02be-de65-4fd5...@d7g2000vbv.googlegroups.com...
So what's the radius of a sphere of volume 1? That will enable you to
discover the area of a sphere of volume 1, and it will then be fairly
simple to determine whether it is larger or smaller than 6.
> Surface area is 4 x pi x radius squared (though I had to look that one up).
>
> So given the direction of this thread, does that make a sphere four times
> the size of a circle?
Not if you work the 4 and the 4/3 right.
> "Peter T. Daniels" <gramma...@verizon.net> wrote in messagenews:ec3e02be-de65-4fd5...@d7g2000vbv.googlegroups.com...
discover the area of a sphere of volume 1, and it will then be fairly
simple to determine whether it is larger or smaller than 6.
> Surface area is 4 x pi x radius squared (though I had to look that one up).
>
> So given the direction of this thread, does that make a sphere four times
> the size of a circle?
Guy Barry
Aug 19, 2012, 1:34:22 PM8/19/12
to
"Peter T. Daniels" wrote in message
--
Guy Barry
Peter T. Daniels
Aug 19, 2012, 1:37:50 PM8/19/12
to
On Aug 19, 1:34 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> "Peter T. Daniels" wrote in messagenews:38fc8ce1-6ab6-4a8d...@p5g2000vbl.googlegroups.com...
not to be your grandmother. And then you would never have existed.
(Unless you're adopted, in which case you probably have had four
grandmothers.)
> "Peter T. Daniels" wrote in messagenews:38fc8ce1-6ab6-4a8d...@p5g2000vbl.googlegroups.com...
> > On Aug 19, 12:43 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> > > Set theory isn't typed. You can have a set whose members are 1 and my
> > > grandmother. (Probably not much use, but the set is well-defined.)
> > You probably have had two grandmothers.
>
> No. My father's mother died before I was born.
She would have had to die before your father was born in order for her
> > > Set theory isn't typed. You can have a set whose members are 1 and my
> > > grandmother. (Probably not much use, but the set is well-defined.)
> > You probably have had two grandmothers.
>
> No. My father's mother died before I was born.
not to be your grandmother. And then you would never have existed.
(Unless you're adopted, in which case you probably have had four
grandmothers.)
Peter T. Daniels
Aug 19, 2012, 1:24:58 PM8/19/12
to
On Aug 19, 9:54 am, Jerry Friedman <jerry_fried...@yahoo.com> wrote:
> Mine does. Intuitively, as you make a rectangle thinner, it
> approaches a line segment, and its area approaches 0.
Asymptotes again. If it actually _becomes_ a line segment, its area
> Mine does. Intuitively, as you make a rectangle thinner, it
> approaches a line segment, and its area approaches 0.
ceases to exist.
Guy Barry
Aug 19, 2012, 1:49:47 PM8/19/12
to
"Peter T. Daniels" wrote in message
> On Aug 19, 1:34 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> > "Peter T. Daniels" wrote in
> > messagenews:38fc8ce1-6ab6-4a8d...@p5g2000vbl.googlegroups.com...
> > > You probably have had two grandmothers.
>
> > No. My father's mother died before I was born.
> She would have had to die before your father was born in order for her
> not to be your grandmother. And then you would never have existed.
> (Unless you're adopted, in which case you probably have had four
> grandmothers.)
If we're going to be really accurate here, I was born without a father,
>
> > No. My father's mother died before I was born.
> She would have had to die before your father was born in order for her
> not to be your grandmother. And then you would never have existed.
> (Unless you're adopted, in which case you probably have had four
> grandmothers.)
since my biological father died before I was born; and the mother of the man
who my mother subsequently married (who became my father via adoption) was
dead at the time he married her. I don't normally go into detail about this
but the fact remains that I have never had a paternal grandmother in any
sense that the term is generally understood.
--
Guy Barry
Joachim Pense
Aug 19, 2012, 2:15:59 PM8/19/12
to
Am 19.08.2012 19:22, schrieb Peter T. Daniels:
>
> Zero times infinity is still zero, so you can't attribute a plane's
> area to its infinite number of points EVEN IF you think points do have
> an area of 0 (which they don't; points have no area and so have no
> area size, either).
>
Don't try teaching your grandma how to suck eggs.
>
> Zero times infinity is still zero, so you can't attribute a plane's
> area to its infinite number of points EVEN IF you think points do have
> an area of 0 (which they don't; points have no area and so have no
> area size, either).
>
Joachim
Andrew B
Aug 19, 2012, 2:17:00 PM8/19/12
to
On 19/08/2012 18:22, Peter T. Daniels wrote:
> Zero times infinity is still zero, so you can't attribute a plane's
> area to its infinite number of points EVEN IF you think points do have
> an area of 0 (which they don't; points have no area and so have no
> area size, either).
It's funny that earlier in this thread, you objected to "Le Ton Beau de
> Zero times infinity is still zero, so you can't attribute a plane's
> area to its infinite number of points EVEN IF you think points do have
> an area of 0 (which they don't; points have no area and so have no
> area size, either).
Marot" on the grounds that Hofstadter was pontificating about something
he evidently didn't know much about, when you're clearly quite happy to
do the same thing...
Guy Barry
Aug 19, 2012, 2:29:56 PM8/19/12
to
"Andrew B" wrote in message news:k0raiq$opa$2...@dont-email.me...
> On 19/08/2012 18:22, Peter T. Daniels wrote:
> > Zero times infinity is still zero,
Although there are no doubt people who would claim
that one divided by zero is infinity, so zero times infinity must be one (or
two or indeed any other number you can think of).
> It's funny that earlier in this thread, you objected to "Le Ton Beau de
> Marot" on the grounds that Hofstadter was pontificating about something he
> evidently didn't know much about, when you're clearly quite happy to do
> the same thing...
people.
--
Guy Barry
Mark Brader
Aug 19, 2012, 4:18:10 PM8/19/12
to
Gordon D.:
Guy Barry:
after the techique of paralleling "Eskimos have 100 different words for
'snow'" [yes, we know that's false] with new expressions like "computer
programmers must have 100 different words for 'bug'".
--
Mark Brader | No programming language is Perfect. Perl comes very close.
m...@vex.net | P! e! r! *l?* :-( Not quite "Perfect".
Toronto | -- Brian Ingerson
My text in this article is in the public domain.
>>> Is that anything like adding "-gate" to a noun to describe a
>>> scandal of some sort (after Watergate, even though that was the
>>> name of the hotel...)
>>> scandal of some sort (after Watergate, even though that was the
Guy Barry:
> Is there a generally accepted term for this phenomenon? (At first I thought
> it might be "reanalysis", but that appears to be slightly different.)
Well, the fairly recent coinage "snowclone" is applicable. It's named
> it might be "reanalysis", but that appears to be slightly different.)
after the techique of paralleling "Eskimos have 100 different words for
'snow'" [yes, we know that's false] with new expressions like "computer
programmers must have 100 different words for 'bug'".
--
Mark Brader | No programming language is Perfect. Perl comes very close.
m...@vex.net | P! e! r! *l?* :-( Not quite "Perfect".
Toronto | -- Brian Ingerson
My text in this article is in the public domain.
Peter T. Daniels
Aug 19, 2012, 4:30:20 PM8/19/12
to
On Aug 19, 1:49 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> "Peter T. Daniels" wrote in messagenews:9f9171b2-7aae-4d4a...@r4g2000vbn.googlegroups.com...
The term is "generally understood" to mean the mother of your father.
My mother's father also died several years before I was born, but that
doesn't keep him from being my grandfather!
> "Peter T. Daniels" wrote in messagenews:9f9171b2-7aae-4d4a...@r4g2000vbn.googlegroups.com...
My mother's father also died several years before I was born, but that
doesn't keep him from being my grandfather!
Peter T. Daniels
Aug 19, 2012, 4:33:15 PM8/19/12
to
interpretation, and finding the results concerning the "areas" of
entities with less than two dimensions that I have reported.
Unless, as I already noted, it's a parlor game like 0.9999999999999...
= 0.
Peter T. Daniels
Aug 19, 2012, 4:34:00 PM8/19/12
to
than that a plane inherits its area from the infinity of points
contained in it.
Peter T. Daniels
Aug 19, 2012, 4:31:54 PM8/19/12
to
On Aug 19, 2:29 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
things.
> > It's funny that earlier in this thread, you objected to "Le Ton Beau de
> > Marot" on the grounds that Hofstadter was pontificating about something he
> > evidently didn't know much about, when you're clearly quite happy to do
> > the same thing...
>
> I'm not sure if he knows anything much about anything, except how to annoy
> people.
Look who's talking!
> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
> > On 19/08/2012 18:22, Peter T. Daniels wrote:
> > > Zero times infinity is still zero,
>
> "Zero times infinity" is meaningless, because infinity isn't a number.
> Although there are no doubt people who would claim
> that one divided by zero is infinity, so zero times infinity must be one (or
> two or indeed any other number you can think of).
Divison by zero and multiplication by zero are very, very different
> > > Zero times infinity is still zero,
>
> "Zero times infinity" is meaningless, because infinity isn't a number.
> Although there are no doubt people who would claim
> that one divided by zero is infinity, so zero times infinity must be one (or
> two or indeed any other number you can think of).
things.
> > It's funny that earlier in this thread, you objected to "Le Ton Beau de
> > Marot" on the grounds that Hofstadter was pontificating about something he
> > evidently didn't know much about, when you're clearly quite happy to do
> > the same thing...
>
> I'm not sure if he knows anything much about anything, except how to annoy
> people.
Joachim Pense
Aug 19, 2012, 4:42:34 PM8/19/12
to
details, grab a book on advanced calculus.
Joachim
benl...@ihug.co.nz
Aug 19, 2012, 4:44:12 PM8/19/12
to
On Aug 20, 5:49 am, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
> "Peter T. Daniels" wrote in messagenews:9f9171b2-7aae-4d4a...@r4g2000vbn.googlegroups.com...
You are talking about "having a grandmother", which for you clearly
means a relationship with a living person.
But why should death disqualify either woman from either (i) _being_
your grandmother; or (ii) being a member of a set?
> "Peter T. Daniels" wrote in messagenews:9f9171b2-7aae-4d4a...@r4g2000vbn.googlegroups.com...
means a relationship with a living person.
But why should death disqualify either woman from either (i) _being_
your grandmother; or (ii) being a member of a set?
John Karl
Aug 19, 2012, 5:00:06 PM8/19/12
to
And in any case, 0.999... = 1 is a perfectly good result. In what sense
would it be a "parlor game"?
Mark Brader
Aug 19, 2012, 5:11:04 PM8/19/12
to
"Lewis":
> > How is 0 mass different from no mass? 0 means none. 0 length is no
> > length, and zero area is no area.
"An X has no Y", where X is a thing and Y is a measurement, is ambiguous
in English. It can either mean that the value of Y is 0, or that it is
not meaningful to speak of X having a measurement Y. In other words,
either it means that the Y of an is 0 or that it's undefined.
Evan Kirshenbaum:
> I can't decide whether or not I think that a line doesn't have area or
> whether it has area zero, but I agree with Peter that they're
> different.
Yes.
I see no reason for this to be undefined -- as far as I'm concerned a line
or a point has area 0. But I could live with it being considered undefined.
--
Mark Brader "I'm not good in groups. It's difficult to
Toronto work in a group when you're omnipotent."
m...@vex.net "Deja Q", ST:TNG, Richard Danus
> > How is 0 mass different from no mass? 0 means none. 0 length is no
> > length, and zero area is no area.
"An X has no Y", where X is a thing and Y is a measurement, is ambiguous
in English. It can either mean that the value of Y is 0, or that it is
not meaningful to speak of X having a measurement Y. In other words,
either it means that the Y of an is 0 or that it's undefined.
Evan Kirshenbaum:
> I can't decide whether or not I think that a line doesn't have area or
> whether it has area zero, but I agree with Peter that they're
> different.
Yes.
I see no reason for this to be undefined -- as far as I'm concerned a line
or a point has area 0. But I could live with it being considered undefined.
--
Mark Brader "I'm not good in groups. It's difficult to
Toronto work in a group when you're omnipotent."
m...@vex.net "Deja Q", ST:TNG, Richard Danus
Evan Kirshenbaum
Aug 19, 2012, 5:38:41 PM8/19/12
to
> On Aug 19, 2:29 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
>> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
>> > On 19/08/2012 18:22, Peter T. Daniels wrote:
>> > > Zero times infinity is still zero,
>>
>> "Zero times infinity" is meaningless, because infinity isn't a number.
>> Although there are no doubt people who would claim
>> that one divided by zero is infinity, so zero times infinity must be one (or
>> two or indeed any other number you can think of).
>
> Divison by zero and multiplication by zero are very, very different
> things.
Suppose I pick a random integer. The probabilty that it is any
>> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
>> > On 19/08/2012 18:22, Peter T. Daniels wrote:
>> > > Zero times infinity is still zero,
>>
>> "Zero times infinity" is meaningless, because infinity isn't a number.
>> Although there are no doubt people who would claim
>> that one divided by zero is infinity, so zero times infinity must be one (or
>> two or indeed any other number you can think of).
>
> Divison by zero and multiplication by zero are very, very different
> things.
particular integer specified beforehand, say, 47, is zero, right?
Same for -1,442,468, for 964,023, and so on. Now what happens if I
add up all the values on the number line. I multiply the zero
probability that each of them has by the infinity of values and get a
probability of one that it will be one of them. On the other hand, if
I multiply each one's zero by the infinity of even numbers, I get a
probability of 1/2 that it's one of them.
As Prof. Chung used to insist, in his thick Chinese accent, "Infinity
is not a number!" How it behaves depends on how you get there.
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |The law of supply and demand tells us
SF Bay Area (1982-) |that when the price of something is
Chicago (1964-1982) |artificially set below market level,
|there will soon be none of that thing
evan.kir...@gmail.com |left--as you may have noticed the
|last time you tried to buy something
http://www.kirshenbaum.net/ |for nothing.
| P.J. O'Rourke
António Marques
Aug 19, 2012, 7:22:09 PM8/19/12
to
Jerry Friedman <jerry_f...@yahoo.com> wrote:
> On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
>> I think what you're saying is that there is a way to define 'area' so
> On Aug 18, 6:13 pm, António Marques <ento...@gmail.com> wrote:
>> that it applies to things which's
>
> Heh.
>
>> definition can be used for line segments.
>
> As long as it's clear that "you" includes all mathematicians, except
> possibly for a set of measure 0 :-) For instance, see page 5 at
>
> http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf
>
> for the idea that points have 0 length and "boxes" can have 0 volume.
> (That includes line segments with 0 area, volume, etc.)
>
> This is also stated at Wikipedia, which I generally trust on math, and
> at Mathworld, where it's not quite so explicit as it is in Terence
> Tao's book.
I don't mind at all, nor do I think that anyone does, that you deal with
objects with a value of 0 for one or more of their dimensions, whether or
not it makes rockets fly more easily.
>> That doesn't mean that our concept of line segments admits
>> area.
>
> Mine does. Intuitively, as you make a rectangle thinner, it
> approaches a line segment, and its area approaches 0.
What I think a number of us feel is that there are geometrical concepts in
> Mine does. Intuitively, as you make a rectangle thinner, it
> approaches a line segment, and its area approaches 0.
the public's mind for which it doesn't make sense to speak of a number of
things. We can tell between an empty tesseract and a point, and we'd like
to keep it that way, because the distinction can be useful. If you have no
use for points and empty tesseracts do fine, then by all means keep using
them. Company and context will determine if it's reasonable for you to
refer to them as points.
--
Sent from one of my newsreaders
António Marques
Aug 19, 2012, 7:22:10 PM8/19/12
to
Paul {Hamilton Rooney} <paulv...@snotmail.com> wrote:
> On 19-Aug-12 3:01 PM, Joachim Pense wrote:
>> Am 19.08.2012 04:20, schrieb Peter T. Daniels:
>>> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
>>>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>>>>
>>>>
>>>>
>>>>>> Okay. If you were, you could figure out why your objection above
> On 19-Aug-12 3:01 PM, Joachim Pense wrote:
>> Am 19.08.2012 04:20, schrieb Peter T. Daniels:
>>> On Aug 18, 5:57 pm, Joachim Pense <s...@pense-mainz.eu> wrote:
>>>> Am 18.08.2012 22:37, schrieb Peter T. Daniels:
>>>>
>>>>
>>>>
>>>>>> isn't valid (along the lines of what Joachim Pense said).
>>>>
>>>>> No. A line segment is, by definition, a thing with one and only one
>>>>> dimension.
>>>>
>>>>> An area is, by definition, a property of things with two dimensions.
>>>>
>>>>> Therefore, a line segment cannot have an area (and it is thusT
>>>>> No. A line segment is, by definition, a thing with one and only one
>>>>> dimension.
>>>>
>>>>> An area is, by definition, a property of things with two dimensions.
>>>>
>>>>> meaningless to assign any number at all to "the area of a line
>>>>> segment").
>>>>
>>>> An area is, by definition, a property of _subsets_ of spaces with two
>>>> dimensions (like planes). Lines and points are such subsets, having area
>>>> zero. A cube is not a subset of a two-dimensional space.
>>>
>>> An area is, by definition, a property of some subsets of spaces with
>>> two dimensions?
>>>
>>> How can things with one and zero dimensions be subsets of things with
>>> two dimensions? They don't _have_ two dimensions!
>>>
>>
>> A plane is a set of points. A triangle in that plane is a subset of the
>> plane. A line in that plane is another subset of the plane. 1000
>> arbitrary isolated points are yet another subset of the plane.
>>
>> Joachim
>>>>> segment").
>>>>
>>>> An area is, by definition, a property of _subsets_ of spaces with two
>>>> dimensions (like planes). Lines and points are such subsets, having area
>>>> zero. A cube is not a subset of a two-dimensional space.
>>>
>>> An area is, by definition, a property of some subsets of spaces with
>>> two dimensions?
>>>
>>> How can things with one and zero dimensions be subsets of things with
>>> two dimensions? They don't _have_ two dimensions!
>>>
>>
>> A plane is a set of points. A triangle in that plane is a subset of the
>> plane. A line in that plane is another subset of the plane. 1000
>> arbitrary isolated points are yet another subset of the plane.
>>
>
>
>
> No it isn't.
> Points have no area. A million points have no area.
> We're talking apples and cuttlefish here, if you'll pardon the phrase.
They're claiming that an infinite number of points have area, because their
>
>
> No it isn't.
> Points have no area. A million points have no area.
> We're talking apples and cuttlefish here, if you'll pardon the phrase.
supposed zero area times infinity is a positive number. I think thats wrong
on more than one level. One, that they really have no area. Two, that
admitting for the sake of notation that they can be considered to have an
area of zero, that is, if we're still talking about points, a constant
zero, not an approximation, so it will remain zero even if multiplied by
infinity. Third, that 'area' arises from the increase in dimensionality,
and the points themselves are not responsible for it, so the area isn't
ever contributed by them. Now, if someone cares to discuss where does
'matter' come from...
António Marques
Aug 19, 2012, 7:22:10 PM8/19/12
to
"Guy Barry" <guy....@blueyonder.co.uk> wrote:
> "Andrew B" wrote in message news:k0raiq$opa$2...@dont-email.me...
>
>> On 19/08/2012 18:22, Peter T. Daniels wrote:
>
>>> Zero times infinity is still zero,
>
> "Zero times infinity" is meaningless, because infinity isn't a number.
> Although there are no doubt people who would claim
> that one divided by zero is infinity, so zero times infinity must be one
> (or two or indeed any other number you can think of).
Wrong. When the zero we're talking about _is_ a number rather than a limit,
> "Andrew B" wrote in message news:k0raiq$opa$2...@dont-email.me...
>
>> On 19/08/2012 18:22, Peter T. Daniels wrote:
>
>>> Zero times infinity is still zero,
>
> "Zero times infinity" is meaningless, because infinity isn't a number.
> Although there are no doubt people who would claim
> that one divided by zero is infinity, so zero times infinity must be one
> (or two or indeed any other number you can think of).
then there's no indetermination and it will be still zero even if times
infinity.
António Marques
Aug 19, 2012, 7:22:11 PM8/19/12
to
Evan Kirshenbaum <evan.kir...@gmail.com> wrote:
> "Peter T. Daniels" <gram...@verizon.net> writes:
>
>> On Aug 19, 2:29 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
>>> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
>>>> On 19/08/2012 18:22, Peter T. Daniels wrote:
>>>>> Zero times infinity is still zero,
>>>
>>> "Zero times infinity" is meaningless, because infinity isn't a number.
>>> Although there are no doubt people who would claim
>>> that one divided by zero is infinity, so zero times infinity must be one (or
>>> two or indeed any other number you can think of).
>>
>> Divison by zero and multiplication by zero are very, very different
>> things.
>
> Suppose I pick a random integer. The probabilty that it is any
> particular integer specified beforehand, say, 47, is zero, right?
No...
> "Peter T. Daniels" <gram...@verizon.net> writes:
>
>> On Aug 19, 2:29 pm, "Guy Barry" <guy.ba...@blueyonder.co.uk> wrote:
>>> "Andrew B" wrote in messagenews:k0raiq$opa$2...@dont-email.me...
>>>> On 19/08/2012 18:22, Peter T. Daniels wrote:
>>>>> Zero times infinity is still zero,
>>>
>>> "Zero times infinity" is meaningless, because infinity isn't a number.
>>> Although there are no doubt people who would claim
>>> that one divided by zero is infinity, so zero times infinity must be one (or
>>> two or indeed any other number you can think of).
>>
>> Divison by zero and multiplication by zero are very, very different
>> things.
>
> Suppose I pick a random integer. The probabilty that it is any
> particular integer specified beforehand, say, 47, is zero, right?
> As Prof. Chung used to insist, in his thick Chinese accent, "Infinity
> is not a number!" How it behaves depends on how you get there.
It is loading more messages.
0 new messages