Is the set { 1, 0 } equal to the set { 0, 1 } ?

[Timothy Golden]

That's a bit overly specific, but the idea is present. To what degree does the bracket notation inherently impose order on a set, and then is elementhood all that has been declared? Clearly we do not list our alphabet that we speak with here arbitrarily, and every typo that I make whether admited or not as some cleaver goof has a correction listed somewhere in an orderly fashion. Is it only arbitrary that my alphabet is
{ a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }
and is this the alphabet that set theory is communicated from? Is this then not actually a set? And is the order merely happenstance? How strange that such a computationally integral concept could go unapplied when it is clearly readily available.

I could see a cloud type of set theory whereby the elements are randomly arranged with some space between them enclosed in a circle, which certainly does go on diagrammatically in set theory when the intersection of two sets and the union of two sets are explained, though rarely do those notations actually carry serious elements. It so happens that another fairly serious 'set' of elements
{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
exist and that their order is entirely meaningful. Indeed I think we could have some trouble if I were communicating with the set
{ 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
wouldn't we?

Would it then be that
1 + 1 = 3
is so for me but not for you?
Clearly then someone ought to disambiguate.
Yet it seems that the set theorists don't care.
WTFIGOH?

[Ben Bacarisse]

The answer to the question in the subject line is yes.

Timothy Golden <timba...@gmail.com> writes:

> That's a bit overly specific, but the idea is present. To what degree
> does the bracket notation inherently impose order on a set,

In order to avoid any such ambiguity, we define an ordered set to be a
pair (S, R) consisting of a set S and an order relation R on it.

An author could, at the risk of being misunderstood, state that we are
to assume an order relation defined by the way the elements are written.
{1,0} and {0,1} would still denote the same set, but they would also
denote the pairs ({1,0}, >) and ({1,0}, <). However, I wold consider
that to be bad writing.

<snip the rest as it became incoherent as far as I could tell>
--
Ben.

[Timothy Golden]

Thanks Ben for the serious response. Fast too.
Next though, if I ask you to give an instance of a set that lacks order using the bracket notation isn't that impossible?
The order that you pass the elements in becomes meaningful doesn't it?
In that it is the first definition of the set it would make sense that it could be reused regularly.
Checking equality even of a long set of elements would argue for maintaining the original definition.
That order is naturally present in the bracketed form and that this early ordering would go unused seems an informational conflict.
Could I ask why one would throw away a piece of information that was passed in the communication?
And why would it be insisted upon that that information be thrown away when it cannot possibly be thrown away?
Can information theory confront set theory here?

[Timothy Golden]

As I see it then under my own position I would disambiguate bracketed set theory. I would impose an Aleph on all serious elemental sets, and it is in fact those elements that we seek as mathematicians and as physicists. Even as philosophers too. Oh, what, you are but one of three? You are but one of 7 billion in the present form. That ten or a hundred or a thousand have spoken before me does not obviate my freedom to construct. Without it you are doomed. The study of regurgitation is not really very well regarded is it? I mean do you like to barf up at the breakfast table on a daily basis? If you were guilty of some mental transgression en masse and I called you on it then will there be some millions barfing up their breakfast tomorrow morning? Ah, you will be a statistic then. Traceable to my post here, and the hypnotic word form that we use will be fully established.

In reality I mean you no harm and here in this last paragraph I grant you immunity from the breakfast barf scenario if you will just please try to consider the set theory as open implying really merely this freedom to construct. Thus you are granted the freedom to construct.
Peace Be With You.

- benevolently, Tim

[Peter]

Timothy Golden wrote:
> That's a bit overly specific, but the idea is present. To what degree does the bracket notation inherently impose order on a set, and then is elementhood all that has been declared? Clearly we do not list our alphabet that we speak with here arbitrarily, and every typo that I make whether admited or not as some cleaver goof has a correction listed somewhere in an orderly fashion. Is it only arbitrary that my alphabet is
> { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }
> and is this the alphabet that set theory is communicated from? Is this then not actually a set? And is the order merely happenstance? How strange that such a computationally integral concept could go unapplied when it is clearly readily available.
>
> I could see a cloud type of set theory whereby the elements are randomly arranged with some space between them enclosed in a circle, which certainly does go on diagrammatically in set theory when the intersection of two sets and the union of two sets are explained, though rarely do those notations actually carry serious elements. It so happens that another fairly serious 'set' of elements
> { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
> exist and that their order is entirely meaningful. Indeed I think we could have some trouble if I were communicating with the set
> { 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
> wouldn't we?

{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } and { 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
are the same set. That follows from the axiom of extensionality:

(forall x)(x in y <-> x in z) -> y = z

Ordered sets are sometime notated, e.g., <0, 1, 2, 3, 4, 5, 6, 7, 8, 9>

> Would it then be that
> 1 + 1 = 3
> is so for me

I wouldn't be at all surprised.

> but not for you?
> Clearly then someone ought to disambiguate.
> Yet it seems that the set theorists don't care.
> WTFIGOH?
>

--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays

[Peter]

Timothy Golden wrote:
> On Thursday, February 11, 2021 at 11:49:12 AM UTC-5, Ben Bacarisse wrote:
>> The answer to the question in the subject line is yes.
>> Timothy Golden <timba...@gmail.com> writes:
>>
>>> That's a bit overly specific, but the idea is present. To what degree
>>> does the bracket notation inherently impose order on a set,
>> In order to avoid any such ambiguity, we define an ordered set to be a
>> pair (S, R) consisting of a set S and an order relation R on it.
>>
>> An author could, at the risk of being misunderstood, state that we are
>> to assume an order relation defined by the way the elements are written.
>> {1,0} and {0,1} would still denote the same set, but they would also
>> denote the pairs ({1,0}, >) and ({1,0}, <). However, I wold consider
>> that to be bad writing.
>>
>> <snip the rest as it became incoherent as far as I could tell>
>> --
>> Ben.
>
> Thanks Ben for the serious response. Fast too.
> Next though, if I ask you to give an instance of a set that lacks order using the bracket notation isn't that impossible?

No. Confusing symbols and things symbolized seems to be a popular
pastime in sci.math (e.g., see parts of the 'Why isn't pi an exact
number ?' thread). Here is a symbol (symbol-complex, if you like) for a
particular unordered set: {0,1,2,3}. The order is *on the screen*. If
you read it out loud the order will be *in the sounds*.

Let's suppose you drink your coffee with milk and sugar. Do you think
that if you drink your coffee with sugar and milk, you are drinking
something else? If your shopping list says 'bread, butter, lamb chops',
do you think you've shopped wrongly (or the list was wrong) if you buy
the lamb chops first? Language, written and spoken, imposes an order.
This was *never* been a problem for you until you came across set notation.

You will fail to get this for the next six months.

> The order that you pass the elements in becomes meaningful doesn't it?
> In that it is the first definition of the set it would make sense that it could be reused regularly.
> Checking equality even of a long set of elements would argue for maintaining the original definition.
> That order is naturally present in the bracketed form and that this early ordering would go unused seems an informational conflict.
> Could I ask why one would throw away a piece of information that was passed in the communication?
> And why would it be insisted upon that that information be thrown away when it cannot possibly be thrown away?
> Can information theory confront set theory here?
>

[Jim Carrubba]

Timothy Golden wrote:

> alphabet that we speak with here arbitrarily, and every typo that I make
> whether admited or not as some cleaver goof has a correction listed
> somewhere in an orderly fashion. Is it only arbitrary that my alphabet
> is { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v,
> w, x, y, z }

Here we go, one more time. Create Your Own Nasal Inhaler to Beat
Congestion (Natural Decongestant). And Biden to impose domestic travel
restriction. Europeans: "First time?".

Btw, it looks like they are using *doppelgängers*. Biden looks like a
different guy, bill gates younger smoother face skin, his husband melinda
much uglier, hilary younger and healthier, the pope like a hologram, the
queen of england like a completely different reptile, henry kissinger,
how old is he now, 200 years?

[Gus Gassmann]

On Thursday, 11 February 2021 at 15:20:31 UTC-4, Peter wrote:
> Let's suppose you drink your coffee with milk and sugar. Do you think
> that if you drink your coffee with sugar and milk, you are drinking
> something else?

Ahem!!! There are any number of people who will tell you that tea and milk is not the same as milk and tea.

[mitchr...@gmail.com]

That is a backward set order...

[Peter]

Peter wrote:
> [...]

> This was *never* been a problem for you until you came across set notation.

Yuk. Either

This was *never* a problem for you until you came across set notation.

or

This has *never* been a problem for you until you came across set notation.

[Ben Bacarisse]

Timothy Golden <timba...@gmail.com> writes:

> On Thursday, February 11, 2021 at 11:49:12 AM UTC-5, Ben Bacarisse wrote:
>> The answer to the question in the subject line is yes.
>> Timothy Golden <timba...@gmail.com> writes:
>>
>> > That's a bit overly specific, but the idea is present. To what degree
>> > does the bracket notation inherently impose order on a set,
>> In order to avoid any such ambiguity, we define an ordered set to be a
>> pair (S, R) consisting of a set S and an order relation R on it.
>>
>> An author could, at the risk of being misunderstood, state that we are
>> to assume an order relation defined by the way the elements are written.
>> {1,0} and {0,1} would still denote the same set, but they would also
>> denote the pairs ({1,0}, >) and ({1,0}, <). However, I wold consider
>> that to be bad writing.
>>
>> <snip the rest as it became incoherent as far as I could tell>
>> --
>> Ben.

(You should not usually quote sig lines.)

> Thanks Ben for the serious response. Fast too.
> Next though, if I ask you to give an instance of a set that lacks
> order using the bracket notation isn't that impossible?

No. Sets have no order. They just have members. { x mod 2 | x in N }
is the same set as the other ways you've written it.

--
Ben.

[FromTheRafters]

Timothy Golden laid this down on his screen :

> That's a bit overly specific, but the idea is present.

Yes, inasmuch as a subset of each can be a subset of the other.

[Timothy Golden]

I'm sorry Ben but you have failed to instantiate.
Thereby you have falsified your own falsification here.
You are treading in doubly ambiguous territory.
Yes; you have the status quo power position.
As underdog I have a peculiar position of unlikelihood.

[Timothy Golden]

When one letter in a description of a set holds so much as the utterance of 'N' then clearly we have exceeded elemental status.
Obviously the level of complexity that you have risen to in order to win this argument is indicative of a problem.
What then is elemental?
As I've said before that which is elemental is of great interest and virtuosity to all.

In order to drive your short description you are resting on rather a lot. I would argue therefor that you are not practicing elemental set theory, whereas I am. I am taking a very careful second look at the assumptions of set theory as we has congealed circa 2020.
I have likewise taken a careful look at operator theory and I do find problems with the binary operator; again congealed circa 2020.
I have likewise taken a careful look at the signature of the real number and I do find problems with it; congealed circa 2020 and going back four hundred years from the present. It is as if man attempts to sink his feet in mortar; generation after generation. It is thus that I must declare the freedom to construct as much as I must likewise declare the freedom to falsify.

[Ben Bacarisse]

(Again, you should not usually quote sig lines.)

> I'm sorry Ben but you have failed to instantiate.

No need to be sorry. You asked a question and answered to the best of
my ability.

--
Ben.

[Timothy Golden]

Holy Carrubba. This is some serious slam down.
WTFIGOHQ

[Timothy Golden]

Y. Y. Y. Y. Y. Y. Y. Y...

[Timothy Golden]

On Friday, February 12, 2021 at 10:33:36 AM UTC-5, Ben Bacarisse wrote:
> Timothy Golden <timba...@gmail.com> writes:
>
> > On Thursday, February 11, 2021 at 4:48:00 PM UTC-5, Ben Bacarisse wrote:
> >> Timothy Golden <timba...@gmail.com> writes:
> >>
> >> > On Thursday, February 11, 2021 at 11:49:12 AM UTC-5, Ben Bacarisse wrote:
> >> >> The answer to the question in the subject line is yes.
> >> >> Timothy Golden <timba...@gmail.com> writes:
> >> >>
> >> >> > That's a bit overly specific, but the idea is present. To what degree
> >> >> > does the bracket notation inherently impose order on a set,
> >> >> In order to avoid any such ambiguity, we define an ordered set to be a
> >> >> pair (S, R) consisting of a set S and an order relation R on it.
> >> >>
> >> >> An author could, at the risk of being misunderstood, state that we are
> >> >> to assume an order relation defined by the way the elements are written.
> >> >> {1,0} and {0,1} would still denote the same set, but they would also
> >> >> denote the pairs ({1,0}, >) and ({1,0}, <). However, I wold consider
> >> >> that to be bad writing.
> >> >>
> >> >> <snip the rest as it became incoherent as far as I could tell>
> >> >> --

> >> >> Been.

> >> (You should not usually quote sig lines.)
> >> > Thanks Ben for the serious response. Fast too.
> >> > Next though, if I ask you to give an instance of a set that lacks
> >> > order using the bracket notation isn't that impossible?
> >> No. Sets have no order. They just have members. { x mod 2 | x in N }
> >> is the same set as the other ways you've written it.
> >>
> >> --

> >> Been.

> (Again, you should not usually quote sig lines.)
> > I'm sorry Ben but you have failed to instantiate.
> No need to be sorry. You asked a question and answered to the best of
> my ability.
>
> --

> Been.

I C so U give up. When the up arrow on our keyboard starts typing out an up arrow glyph we will have some serious trouble won't we?

[Ben Bacarisse]

Timothy Golden <timba...@gmail.com> writes:

> On Friday, February 12, 2021 at 10:33:36 AM UTC-5, Ben Bacarisse wrote:
>> > On Thursday, February 11, 2021 at 4:48:00 PM UTC-5, Ben Bacarisse wrote:
>> >> > On Thursday, February 11, 2021 at 11:49:12 AM UTC-5, Ben Bacarisse wrote:

>> >> >> --
>> >> >> Been.
<cut>
>> >> --
>> >> Been.
<cut>
>> --
>> Been.

I normally remind you (again) not to quote sigs here, but you've changed
my name. In the old quotes. I'm hoping that's an accident.

> I C so U give up.

What? Are you six? I answered your question as best I could. You
either didn't like the answer, were sure I was wrong or didn't
understand it. That's fine, but there's not much more I can do to help.

--
Ben.

[Peter]

Timothy Golden wrote:

> [...] I am taking a very careful second look at the assumptions of

> set theory as we has congealed circa 2020. I have likewise taken a
> careful look at operator theory and I do find problems with the
> binary operator; again congealed circa 2020. I have likewise taken a
> careful look at the signature of the real number and I do find
> problems with it; congealed circa 2020 and going back four hundred
> years from the present.

May I ask what form these "careful looks" take? Have you read anything?
Also, what is operator theory? And what is the signature of the real
number?

[Timothy Golden]

On Friday, February 12, 2021 at 3:22:01 PM UTC-5, Peter wrote:
> Timothy Golden wrote:
>
> > [...] I am taking a very careful second look at the assumptions of
> > set theory as we has congealed circa 2020. I have likewise taken a
> > careful look at operator theory and I do find problems with the
> > binary operator; again congealed circa 2020. I have likewise taken a
> > careful look at the signature of the real number and I do find
> > problems with it; congealed circa 2020 and going back four hundred
> > years from the present.
> May I ask what form these "careful looks" take? Have you read anything?
> Also, what is operator theory? And what is the signature of the real
> number?
> --

> When, twice, reference was made to a statesman almost universally

> recognized as one of the villains of this century, in order to
> induce him to a negative judgment, he replied: "My situation is
> so different from his, that it is not for me to pass judgment".
> Ernst Specker on Paul Bernays

Totally inauthentic Peter. It is as if our discussion in abstract algebra meant absolutely nothing to you.
You are a nothing burger.
What was that tail about that I happened to find?
Oh yes, the goose.....
The black goose.
Wasn't that a trip?

So many angles to play when things go wrong. Just like in software. Side-effects are everywhere while the invalid assumption sits there unattended.

[Chris M. Thomasson]

lol!

[Sergio]

that is illegal in all 50 states, and will get you banned by Tweeter

> Thereby you have falsified your own falsification here.

two falsifies make a un-falsified

> You are treading in doubly ambiguous territory.

which type of "treading", foots or water or ... ?

[Sergio]

do you always write in old sayings ?

>Just like in software. Side-effects are everywhere while the invalid assumption sits there unattended.

poorly worded sentence, try again.

[Wade Brewer]

Sergio wrote:
>> I'm sorry Ben but you have failed to instantiate.
> that is illegal in all 50 states, and will get you banned by Tweeter
>> Thereby you have falsified your own falsification here.
> two falsifies make a un-falsified
>> You are treading in doubly ambiguous territory.
> which type of "treading", foots or water or ... ?

China’s Tianwen-1 spacecraft was launched toward Mars in July 2020 from
the Wenchang Space Launch Center, and successfully entered the red
planet’s orbit on Wednesday. The 5-ton probe (that's alot of probe) isn’t
expected to land on the Martian surface until sometime in May.

No more fake "martian" probes tv from Alaska. I love the Chinese so very
much. Just think, a traitor CIA agent Gorbachev in prosperous china now,
will destroy and bring those people into deep poverty, enslaved into
eternity the "new normal" *neo-feudal* capitalism.

I just put my trust in China, the only hope we have left. Just amazing how
things turns out. Bravo China.

[Timothy Golden]

Possibly the next brew-ha will be whose bot gets to ride on a long term adventure and run the show. Humans in space makes about as much sense as with wax wings flying toward the sun.
https://en.wikipedia.org/wiki/Icarus

But here the issues that I take up with set theory are not getting falsified are they?
Ben starts out here strong but has gone out with a whimper.

I must ask again: Can information theory trump set theory?

[Peter]

Timothy Golden wrote:
> On Friday, February 12, 2021 at 3:22:01 PM UTC-5, Peter wrote:
>> Timothy Golden wrote:
>>
>>> [...] I am taking a very careful second look at the assumptions of
>>> set theory as we has congealed circa 2020. I have likewise taken a
>>> careful look at operator theory and I do find problems with the
>>> binary operator; again congealed circa 2020. I have likewise taken a
>>> careful look at the signature of the real number and I do find
>>> problems with it; congealed circa 2020 and going back four hundred
>>> years from the present.
>> May I ask what form these "careful looks" take? Have you read anything?
>> Also, what is operator theory? And what is the signature of the real
>> number?
>> --
>> When, twice, reference was made to a statesman almost universally
>> recognized as one of the villains of this century, in order to
>> induce him to a negative judgment, he replied: "My situation is
>> so different from his, that it is not for me to pass judgment".
>> Ernst Specker on Paul Bernays
>

(i) Your newsreader should delete my sig.

> Totally inauthentic Peter. It is as if our discussion in abstract algebra meant absolutely nothing to you.

(ii) You have taken a careful look (your words) at operator theory and
you cannot say what it is? Ditto the signature of the real number.

> You are a nothing burger.

I don't know what that means. What has it got to do with your
(apparently inexplicable) claims?

> What was that tail about that I happened to find?
> Oh yes, the goose.....
> The black goose.
> Wasn't that a trip?
>
> So many angles to play when things go wrong. Just like in software. Side-effects are everywhere while the invalid assumption sits there unattended.
>

--
When, once, reference was made to a statesman almost universally

[Sergio]

On 2/13/2021 1:35 AM, Wade Brewer wrote:
> Sergio wrote:
>>> I'm sorry Ben but you have failed to instantiate.
>> that is illegal in all 50 states, and will get you banned by Tweeter
>>> Thereby you have falsified your own falsification here.
>> two falsifies make a un-falsified
>>> You are treading in doubly ambiguous territory.
>> which type of "treading", foots or water or ... ?
>
> China’s Tianwen-1 spacecraft was launched toward Mars in July 2020 from
> the Wenchang Space Launch Center, and successfully entered the red
> planet’s orbit on Wednesday. The 5-ton probe (that's alot of probe) isn’t
> expected to land on the Martian surface until sometime in May.

A FAKE CCP commie plot with FAKE red planet, which is really a mellon
painted with red house paint.

>
> No more fake "martian" probes tv from Alaska. I love the Chinese so very
> much.

yes, they smarter than you. You buy all your (chinese) stuff at Wallmart

> Just think, a traitor CIA agent Gorbachev in prosperous china now,
> will destroy and bring those people into deep poverty, enslaved into
> eternity the "new normal" *neo-feudal* capitalism.

you will reach your "new normal" w free lobotomy, just like Biden did.

>
> I just put my trust in China, the only hope we have left. Just amazing how
> things turns out. Bravo China.
>

they are going to be hard to beet

[Sergio]

only teenage girls ware flasifieds

> Ben starts out here strong but has gone out with a whimper.
>
> I must ask again: Can information theory trump set theory?

Trump was setup, no theory.

>

[Timothy Golden]

Very Much So Sir.
Very Very Good.
Very Very Very Very Very Very Good.
Very Very Very
Very Very Very Very
Very Very Very Very Good.
Very Very Very Very
Very, Very, Very
Very Very Very Very
Very Good.

>
> >

[Timothy Golden]

> >> Bern.

> (Again, you should not usually quote sig lines.)
> > I'm sorry Ben but you have failed to instantiate.
> No need to be sorry. You asked a question and answered to the best of
> my ability.
>
> --

> Bern.

Hey Bacarisse;
Hey Ba ca ri say;
Hey Ba ca ri see;
Hey, Ba ca ri say;
Hey hey, ba ca ri see;
Hey, Ba ca ri say;

All Good Monkeys Have Persistence
... As ...
Every Good Boy Deserves Fudge
Practice your scales thriceaday
and never be out of tune.
There are but twelve and all others are bad.
Thus it is that a false set has been laid upon us.
One practiced by masters and maistroes.
Ever dirty hoes among us know those tones.
Please take out the white trash; the black trash; the yellow trash; the red trash; the green trash (I believe the new SETI has something to say here recently doesn't it?) Possibly some of the off-white trash could go too.

[Timothy Golden]

Why six, Ben? Six carries some deep congruities; arguably seven would be giving me a bit more credit. But six? How did you do that? How dare you?

[Timothy Golden]

Well, Peter, I appreciate you not black-listing me.
By the way it was a swan; not a goose.
Possibly your bot styled training has wiped your memory bank clean of the past conflicts that we have engaged in here.
Certainly my own banks have wiped your memory as a piss-mouse kind of mouse shit left in my eating bowl over the course of months; sitting untouched near the kitchen sink. I hate to do dishes.

[Python]

You are insane.

[Timothy Golden]

On Thursday, February 11, 2021 at 2:20:31 PM UTC-5, Peter wrote:
> Timothy Golden wrote:

> > On Thursday, February 11, 2021 at 11:49:12 AM UTC-5, Ben Bacarisse wrote:

> >> The answer to the question in the subject line is yes.
> >> Timothy Golden <timba...@gmail.com> writes:
> >>
> >>> That's a bit overly specific, but the idea is present. To what degree
> >>> does the bracket notation inherently impose order on a set,
> >> In order to avoid any such ambiguity, we define an ordered set to be a
> >> pair (S, R) consisting of a set S and an order relation R on it.
> >>
> >> An author could, at the risk of being misunderstood, state that we are
> >> to assume an order relation defined by the way the elements are written.
> >> {1,0} and {0,1} would still denote the same set, but they would also
> >> denote the pairs ({1,0}, >) and ({1,0}, <). However, I wold consider
> >> that to be bad writing.
> >>
> >> <snip the rest as it became incoherent as far as I could tell>
> >> --
> >> Ben.
> >

> > Thanks Ben for the serious response. Fast too.
> > Next though, if I ask you to give an instance of a set that lacks order using the bracket notation isn't that impossible?

> No. Confusing symbols and things symbolized seems to be a popular
> pastime in sci.math (e.g., see parts of the 'Why isn't pi an exact
> number ?' thread).

Ahhh.... Here I find something of importance, though topped in mouse shit.
You speak of:
" Confusing symbols and things symbolized"
and this is rather quite something that you speak of in our pure alphabetic form thusly 'monetizing' 39 tokens each comprising approximately but less than 5 bits of information. Thus in its entirety this statement must be composed of less than 199 bits of information, correct? This sort of 1 byte strategy; a sound bytet from heaven; this is exactly what we are after I think.

I must ask you for more of your thinking here. Please raise the bit count. Rather, can we compress it?
Representation
comes to mind, and here I have engaged 14 tokens; forgoing the upper-case which I assume all will grant, as in the eightees where all this crap started.


> Here is a symbol (symbol-complex, if you like) for a
> particular unordered set: {0,1,2,3}. The order is *on the screen*. If
> you read it out loud the order will be *in the sounds*.

>
> Let's suppose you drink your coffee with milk and sugar. Do you think
> that if you drink your coffee with sugar and milk, you are drinking

> something else? If your shopping list says 'bread, butter, lamb chops',
> do you think you've shopped wrongly (or the list was wrong) if you buy
> the lamb chops first? Language, written and spoken, imposes an order.

> This was *never* been a problem for you until you came across set notation.
>

> You will fail to get this for the next six months.
> > The order that you pass the elements in becomes meaningful doesn't it?
> > In that it is the first definition of the set it would make sense that it could be reused regularly.
> > Checking equality even of a long set of elements would argue for maintaining the original definition.
> > That order is naturally present in the bracketed form and that this early ordering would go unused seems an informational conflict.
> > Could I ask why one would throw away a piece of information that was passed in the communication?
> > And why would it be insisted upon that that information be thrown away when it cannot possibly be thrown away?
> > Can information theory confront set theory here?

[Timothy Golden]

I'm taking this as a complement.

[FromTheRafters]

Timothy Golden was thinking very hard :

Oh, good, some math. A complement to what?

[Sergio]

hmmm.... only Very Good ?
not Excellent ? not Extremely Great ?
comedy is hard to do... (some comic said that)

[Timothy Golden]

Properly it is spoken with a fairly quick rhythm. If you get it right it catches you and you can ride it for a while. It's not really such a bad mantra; presuming it to be applied to some truth, that is. For the mistaken; well; I suppose we all are such at some level. We should then just settle on it as a positive aspiration rather than petting ones ego, please.

[Peter]

Timothy Golden wrote:
> [...]

> I'm taking this as a complement.

And I'm taking that as a misspelling of "compliment". I count myself
among the world's worst spellers, so normally I feel that I have no
business commenting on such things, but it amuses me that it appears in
a thread on sets.

You're still failing to delete sigs.

[Burl Scheibe]

Sergio wrote:

>> China’s Tianwen-1 spacecraft was launched toward Mars in July 2020 from
>> the Wenchang Space Launch Center, and successfully entered the red
>> planet’s orbit on Wednesday. The 5-ton probe (that's alot of probe)
>> isn’t expected to land on the Martian surface until sometime in May.
>
> A FAKE CCP commie plot with FAKE red planet, which is really a mellon
> painted with red house paint.
>
>> No more fake "martian" probes tv from Alaska. I love the Chinese so
>> very much.
>
> yes, they smarter than you. You buy all your (chinese) stuff at Wallmart

Years ago Texas Instruments and others gave samples for free. Not
anymore. All the free samples you get now are from The Peoples Republic
of China. By the people, to the people. A verifiable standard of living
indicator.

[Timothy Golden]

DigiKey sent me a nice PCB ruler with all the gauges of circuit printing on it. For instance did you know that an M6 thread will fit tightly through a 6.4mm hole? That a #10 screw happens to be 5.0mm on the nose? That AWG#30 7 strand wire will fit through a 0.305 mm hole? #10AWG 2.95 mm
but I'm not sure what the little null ahead of the number means. Possibly it is actually a 3.0mm hole on the ruler. Each one is a gold plated via. Maybe about thirty of them in total. Pads to 0.4mm, passives down to '0201 (0603m)'. It's difficult to visualize the shrinkage that is taking place year by year. Those who are in this realm simply live through it. I remember the days of the office lunch pizza and somebody tells a story of punch card days; how so and so spilt a giant box of cards; hand-punched; well; you've got to decide whether to start over from scratch or to deshuffle them. You hope for the deshuffle and then when you get a bug you are really fucked. Of course that was the case anyways right?

The answer my friends as to how all of this takes place is incrementally and repeatably. The drive really must be reallocated away from capitalism for this is pure technology we speak of. When the capitalists rape our technology only bad comes of it. Take the phone networks for instance. Ripe for take-over you say? Now, hold on a minute, what were all those standards really about? They were coming like gangbusters when I was in college in the journals circa 1990. Linus Torvalds came to campus and I got his autograph on an early linux distro he was giving out. I still have myriad; coprocessor and all. Damned if I could remember the passwords though.

Got Ring Around The Kernel? Get It Out with the latest CIA Kangaroo Release!

[Timothy Golden]

On Thursday, February 11, 2021 at 11:37:15 AM UTC-5, Timothy Golden wrote:
> That's a bit overly specific, but the idea is present. To what degree does the bracket notation inherently impose order on a set, and then is elementhood all that has been declared? Clearly we do not list our alphabet that we speak with here arbitrarily, and every typo that I make whether admited or not as some cleaver goof has a correction listed somewhere in an orderly fashion. Is it only arbitrary that my alphabet is
> { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }
> and is this the alphabet that set theory is communicated from? Is this then not actually a set? And is the order merely happenstance? How strange that such a computationally integral concept could go unapplied when it is clearly readily available.
>
> I could see a cloud type of set theory whereby the elements are randomly arranged with some space between them enclosed in a circle, which certainly does go on diagrammatically in set theory when the intersection of two sets and the union of two sets are explained, though rarely do those notations actually carry serious elements. It so happens that another fairly serious 'set' of elements
> { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
> exist and that their order is entirely meaningful. Indeed I think we could have some trouble if I were communicating with the set
> { 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
> wouldn't we?
>
> Would it then be that
> 1 + 1 = 3
> is so for me but not for you?
> Clearly then someone ought to disambiguate.
> Yet it seems that the set theorists don't care.
> WTFIGOH?

So today I've gotten myself wondering:
If set theory is granted inherent order then what in mathematics gets obviated?
I honestly have no idea, but no doubt from an axiomatic point of view a restructuring would take place.
The damn func()ers have run away with all the fundamentals and that is not good.
The notion of D:
https://en.wikipedia.org/wiki/Domain_of_discourse
suggests that no second set is necessary, and this awareness is completely oblivious to elemental analysis.
If we get the elements right then should everything fall into place, as it were?
What? flat? no hierarchy whatsoever? Bullshit.
Any who are hunting down a finite list of axioms as universal are practicing flat-earth philosophy.
The whole point is that the thing is structured.
Spacetime is structured, good sirs.
It is thus that the first cosmologican principle is a fraud.
Oh my.
How Odd.

[Eddy Scolaro]

Timothy Golden wrote:

>> > yes, they smarter than you. You buy all your (chinese) stuff at
>> > Wallmart
>> Years ago Texas Instruments and others gave samples for free. Not
>> anymore. All the free samples you get now are from The Peoples Republic
>> of China. By the people, to the people. A verifiable standard of living
>> indicator.
>
> DigiKey sent me a nice PCB ruler with all the gauges of circuit printing
> on it. For instance did you know that an M6 thread will fit tightly

For which you paid big time. DigiKey is not a manufacturer. Jump again,
higher.

[Peter]

Timothy Golden wrote:
> [...]

> So today I've gotten myself wondering:
> If set theory is granted inherent order then what in mathematics gets obviated?

In set theory an obvious way of defining an order is
x < y iff x in y
That "in" is the stylized epsilon read as "is an element of". It fails
to have some of the properties that one might want of an order. E.g.
trichotomy (that's "just one of x < y, x = y, y < x is true") fails.

Another possibility is
x < y iff x propersubset y
but trichotomy still fails.

Among von Neumann ordinals, x in y and x propersubset y coincide and
x < y is defined to be either. Trichotomy does then hold.

> [...]

[Timothy Golden]

On Wednesday, February 17, 2021 at 2:46:32 PM UTC-5, Peter wrote:
> Timothy Golden wrote:
> > [...]
> > So today I've gotten myself wondering:
> > If set theory is granted inherent order then what in mathematics gets obviated?
> In set theory an obvious way of defining an order is
> x < y iff x in y
> That "in" is the stylized epsilon read as "is an element of". It fails
> to have some of the properties that one might want of an order. E.g.
> trichotomy (that's "just one of x < y, x = y, y < x is true") fails.
>
> Another possibility is
> x < y iff x propersubset y
> but trichotomy still fails.
>
> Among von Neumann ordinals, x in y and x propersubset y coincide and
> x < y is defined to be either. Trichotomy does then hold.
>
> > [...]
> --

> When, twice, reference was made to a statesman almost universally

> recognized as one of the villains of this century, in order to
> induce him to a negative judgment, he replied: "My situation is
> so different from his, that it is not for me to pass judgment".
> Ernst Specker on Paul Bernays

I think the converse of my argument might be worth studying. The {} notation of set definitions and elementhood requires that order be implemented as for instance
S1 : { Element2, Element1, Element3 }
and if this bothers you please remember it is the status quo position that the order does not matter. Yet there is order. Informationally speaking our constructions need to be simpler than that which we build. Whereas set theory offends this principle then the converse argument holds that an unordered set must be presentable (i.e. representable) without order. Strangely this is an interdiction on ordinary dimensional theory. For instance we know that objects in three dimensions lack order. We cannot simply derive the order of objects in the room about us. We can arbitrarily assign them, but there is no actual natural order to them. Yes you can devise methods to do it, but they are not universal in nature.

That we grammatically are forced into this unidirectional string of 5 bit tokens is not in keeping with set theory if set theory is pure. That spacetime for instance is not unidirectional could interpose a conflict with this textual method of break down which is inherently unidirectional. Sequential processing is what we do here. It is the form that we inhabit. That nature does not abide by this within her own geometry is a conflict of a sort that some will assign the term 'ontological' to, but in that we can remain first order in this analysis we ought not to jump out away from the very direct form that I attempt here.

The lack of order of a pure set theory does carry this minimal correspondence with reality and yet such a slight detail and its consequences could go overlooked, particularly when purity is claimed on the grammatical form, which is dubious. That set theory ought to rest its case somewhere as deep as information theory goes; yes, I find this believable, but that we are not there yet I also find plausible.

[Peter]

You think that because when you write {w,x,y,z} you must write the
w,x,y,z in _some_ order (such is the nature of writing) that that means
the things denoted by w,x,y,z must be in some order (the same one) also?
That's just confusing the set with the notation.

> Informationally
> speaking our constructions need to be simpler than that which we
> build. Whereas set theory offends this principle then the converse
> argument holds that an unordered set must be presentable (i.e.
> representable) without order.

If by "representable" you mean "capable of being written down in such a
way that all its features are exhibited", I see no reason why that
should be so. I can't represent (in that sense) the unordered set
{w,x,y,z} because the lack of order can't be represented (by our writing
subsystem or any other that I know of). Do you think that because of
that the unordered set {w,x,y,z} is somehow problematic? That's a bit
like people thinking that because the cannot write down all the decimal
digits of pi, pi is somehow problematic ("inexact", apparently).

One needn't always represent a finite set by listing its elements. Do
remember Ben offering { x mod 2 | x in N } as an alternative to {0,1}?

--
When, once, reference was made to a statesman almost universally

[Timothy Golden]

Yes, this language is beyond elemental set theory. Simply uttering 'N' is rather more than elemental.
This is quite another format.

The bracket notation implies that it encloses a list. As such, and upon entering a clean definition, the elements will be passed with some inherent order. Informationally this is in conflict with the pure notion of set that you are clearly expounding on above. This then become a structural argument. We ought to be building more complicated things from simpler things. This is structured thinking and I am simply extending this thought process downward onto set theory. It is not really even an argument that I feel terribly attached to and I am tempted to let up and say, well, yes, Peter, and thank you for spending an authentic moment here... but as I've just reposited my attack I see it again the other way.

Yes, it is a nearly linguistic argument. Even the Kingdom of Animalia comes into some order even if the set is not fully declared. It does so by structure... something entirely lacking within the notion of a set. If an unstructured set cannot be passed in communication then the need to require such disorder in the first place is questionable, no?

I do thank you for turning a little bit of your attention to this, and I do think that is all that it needs. Once again, as in operator theory, we are down deep in the fundamentals. There is not much room here, and yet if integrity is lacking then the results could be dubious. Partially what takes me here I suppose is when elemental set theory is induced via the operator only to be squashed by a functional description of the operator requiring a Cartesian product. A fishy smell emanates.

Again, dimensionality plays some part. Here on this two dimensional medium we can freely scan backward a few paragraphs and refresh something that was initially ignored. Not so of a true unidirectional string that comes flying at you token by token; as in the elemental sense of serious usage of set theory here as we communicate. Lo and behold, the meaning is not in the elements themselves but in their combinational constructions both within and without which are known as words. Well, then, are the words elemental? No. Not here they aren't. But were they at one time? Before the written word? Maybe.

I apologize if you've gotten this far and consider this a digression for I then have wasted your time. Still, possibly there are some consequences to this analysis. I already have proof that structured thought of mathematicians versus the structured mechanisms used in programming as is done through a compiler which requires another level of integrity causes one to double back on the mathematicians. I do not yet curse set theory here.


>
> --
> When, and henceforth, reference was made to a statesman almost universally

> recognized as one of the villains of this century, in order to
> induce him to a negative judgment, he replied: "My situation is
> so different from his, that it is not for me to pass judgment".

> Ernst's pecker on Paul Bernay's wife

[Timothy Golden]

Yes, it is problematic. The problem is that you've spent more information describing the unordered set than you would spend to describe the ordered set. Let's presume that we are not in any Cartesian product space as you've suggested earlier. We are discussing one set S1:
S1 = { w, x, y, z }
though the meaning of these 'elements' is ill defined. Certainly as belated letters of the English alphabet they will pass as authentic elements. Clearly under this interpretation they are not at all a complete set. Some sets do have rather great importance such as the real numbers, for instance, and admittedly they do not take this simplistic notation. Clearly we are settled into a discrete version here. Well, well, we settle for a discrete representation of every concrete value in the reals as well, e.g. 1.2345. This causes yet another conflagration since the elements are actually:
D10 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
and so a discussion on what exactly is elemental ensues, with minor burns only to these digits which incidentally we all operate on as an unstated assumption. In hindsight all of our construction here is composed of combinations of these elemental glyphs. These are not regarded as Cartesian in nature, though arguably a 100 character document could be treated as a 100 dimensional discrete space. In fact when we find errors in typing it exposes that we benefit by not completely filling out that space. For systems like the real numbers we save ourselves quite a lot of time by not asking our students to scribe out values on increments of 0.0001 up to unity. The seemingly futile nature of the concrete form is alleviated by the elemental value 'a' and some neat tricks do develop there, but none of them obviate the usage of concrete values. Clearly such a set carries order, as do most sets, and to insist on disordering a system in order to fully declare it a set is foolhardy IMO.

Under a structured thought perspective we ought to build more complicated things from simpler things. At some point we hope that we achieve such a basic representation as to name that system a basis. At some level we all are in search of the basis. As primates who came down from the tree branches many generations ago we must admit that we are engaged in a progression; a progression from naught which has taken many branches and has accumulated a tremendous pile of informatic content as we see on the internet or in the stacks of the college library. There are fundamental struggles and really lockups as the race condition of those fixated on infinity expose.

If a computer compiler were told of a set of values in say an enumeration, it could go through those values one by one and if it found a match it could provide the functionality that enumerations allow for, typically in a switch(a) statement. However to tell that compiler to disorder an enumeration cannot possibly be a meaningful step.
This is clearly the problem with your language. It is only by convention of contorted humans whose mimicry responses are guaranteed by their social animal form (with linguistic mimicry to boot) that your language is acceptable. There is no compiler level integrity in the history of mathematics. We have now entered the computer age; an age where a compiler error is not something that we fight with. Control theory within a client / server methodology likewise inverts what appears to place the server as a high value asset. And yet the bifurcation is only meaningful in its duplicity. In reality the server side is generally the easy side of things. Too much complexity there will be sure to bungle things up; as in ftp, whereas http did achieve utter simplicity.

In that set theory is to be fundamental in nature it would seem that a quagmire does ensue when you issue the requirement that a set you've just passed in an orderly fashion have most of its information removed. I don't really know that there is that much information left in the elements you've passed other than their order. As tokens go, they are merely tokens in an even playing field via the set status. To say, shuffle them at reception such that the sender has no idea how the receiver keeps them cannot be a wise choice within communication theory. Here I am holding by this idea that information theory could be in conflict with accepted set theory. Yes, we are securing this perspective.

[Sergio]

...DigiKey...

[Peter]

Timothy Golden wrote:
> On Wednesday, February 17, 2021 at 3:55:10 PM UTC-5, Peter wrote:
>> Timothy Golden wrote:
>>> On Wednesday, February 17, 2021 at 2:46:32 PM UTC-5, Peter wrote:
>>>> Timothy Golden wrote:
>>>>> [...] So today I've gotten myself wondering: If set theory is
>>>>> granted inherent order then what in mathematics gets obviated?
>>>> In set theory an obvious way of defining an order is x < y iff x in
>>>> y That "in" is the stylized epsilon read as "is an element of". It
>>>> fails to have some of the properties that one might want of an
>>>> order. E.g. trichotomy (that's "just one of x < y, x = y, y < x is
>>>> true") fails.
>>>>
>>>> Another possibility is x < y iff x propersubset y but trichotomy
>>>> still fails.
>>>>
>>>> Among von Neumann ordinals, x in y and x propersubset y coincide
>>>> and x < y is defined to be either. Trichotomy does then hold.
>>>>
>>>>> [...]
>>>> -- When, twice, reference was made to a statesman almost
>>>> universally recognized as one of the villains of this century, in
>>>> order to induce him to a negative judgment, he replied: "My
>>>> situation is so different from his, that it is not for me to pass
>>>> judgment". Ernst Specker on Paul Bernays

Can you please learn to delete sigs. Your newsreader should do it. If
it, doesn't either get a new one or delete them yourself.

>>> I think the converse of my argument might be worth studying. The {}
>>> notation of set definitions and elementhood requires that order be
>>> implemented as for instance S1 : { Element2, Element1, Element3 } and
>>> if this bothers you please remember it is the status quo position
>>> that the order does not matter. Yet there is order.
>> You think that because when you write {w,x,y,z} you must write the
>> w,x,y,z in _some_ order (such is the nature of writing) that that means
>> the things denoted by w,x,y,z must be in some order (the same one) also?
>> That's just confusing the set with the notation.
>>> Informationally
>>> speaking our constructions need to be simpler than that which we
>>> build. Whereas set theory offends this principle then the converse
>>> argument holds that an unordered set must be presentable (i.e.
>>> representable) without order.
>> If by "representable" you mean "capable of being written down in such a
>> way that all its features are exhibited", I see no reason why that
>> should be so. I can't represent (in that sense) the unordered set
>> {w,x,y,z} because the lack of order can't be represented (by our writing
>> subsystem or any other that I know of). Do you think that because of
>> that the unordered set {w,x,y,z} is somehow problematic?
>
> Yes, it is problematic. The problem is that you've spent more information describing the unordered set than you would spend to describe the ordered set

Only because you're too thick to get these elementary facts: (i) sets
are unordered, (ii) language is ordered.

> . Let's presume that we are not in any Cartesian product space as you've suggested earlier. We are discussing one set S1:
> S1 = { w, x, y, z }
> though the meaning of these 'elements' is ill defined. Certainly as belated letters of the English alphabet they will pass as authentic elements. Clearly under this interpretation they are not at all a complete set. Some sets do have rather great importance such as the real numbers, for instance, and admittedly they do not take this simplistic notation. Clearly we are settled into a discrete version here. Well, well, we settle for a discrete representation of every concrete value in the reals as well, e.g. 1.2345. This causes yet another conflagration since the elements are actually:
> D10 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
> and so a discussion on what exactly is elemental ensues, with minor burns only to these digits which incidentally we all operate on as an unstated assumption. In hindsight all of our construction here is composed of combinations of these elemental glyphs. These are not regarded as Cartesian in nature, though arguably a 100 character document could be treated as a 100 dimensional discrete space. In fact when we find errors in typing it exposes that we benefit by not completely filling out that space. For systems like the real numbers we save ourselves quite a lot of time by not asking our students to scribe out values on increments of 0.0001 up to unity. The seemingly futile nature of the concrete form is alleviated by the elemental value 'a' and some neat tricks do develop there, but none of them obviate the usage of concrete values. Clearly such a set carries order, as do most sets, and to insist on disordering a system in order to fully declare it a set is foolhardy IMO.
>
> Under a structured thought perspective we ought to build more complicated things from simpler things. At some point we hope that we achieve such a basic representation as to name that system a basis. At some level we all are in search of the basis. As primates who came down from the tree branches many generations ago we must admit that we are engaged in a progression; a progression from naught which has taken many branches and has accumulated a tremendous pile of informatic content as we see on the internet or in the stacks of the college library. There are fundamental struggles and really lockups as the race condition of those fixated on infinity expose.
>
> If a computer compiler were told of a set of values in say an enumeration, it could go through those values one by one and if it found a match it could provide the functionality that enumerations allow for, typically in a switch(a) statement. However to tell that compiler to disorder an enumeration cannot possibly be a meaningful step.
> This is clearly the problem with your language. It is only by convention of contorted humans whose mimicry responses are guaranteed by their social animal form (with linguistic mimicry to boot) that your language is acceptable. There is no compiler level integrity in the history of mathematics. We have now entered the computer age; an age where a compiler error is not something that we fight with. Control theory within a client / server methodology likewise inverts what appears to place the server as a high value asset. And yet the bifurcation is only meaningful in its duplicity. In reality the server side is generally the easy side of things. Too much complexity there will be sure to bungle things up; as in ftp, whereas http did achieve utter simplicity.
>
> In that set theory is to be fundamental in nature it would seem that a quagmire does ensue when you issue the requirement that a set you've just passed in an orderly fashion have most of its information removed. I don't really know that there is that much information left in the elements you've passed other than their order. As tokens go, they are merely tokens in an even playing field via the set status. To say, shuffle them at reception such that the sender has no idea how the receiver keeps them cannot be a wise choice within communication theory. Here I am holding by this idea that information theory could be in conflict with accepted set theory. Yes, we are securing this perspective.
>

--
When, once, reference was made to a statesman almost universally

[Hants Wiggins]

Sergio wrote:

>>>> Years ago Texas Instruments and others gave samples for free. Not
>>>> anymore. All the free samples you get now are from The Peoples
>>>> Republic of China. By the people, to the people. A verifiable
>>>> standard of living indicator.
>>>
>>> DigiKey sent me a nice PCB ruler with all the gauges of circuit
>>> printing on it. For instance did you know that an M6 thread will fit
>>> tightly
>>
>> For which you paid big time. DigiKey is not a manufacturer. Jump again,
>> higher.
>
> ...DigiKey...

so you capitalists are thinking, knowingly the evolution worked on the
human immune system for millions of years, yet big capitalist pharma is
trying to convince you that's wrong, by lethally injecting toxic crap
directly into your blood circuitry, bypassing all natural evolved defence
barriers. But the immune systems includes those barriers. What can you
say in your defence? You capitalists are criminals.

[Sergio]

we not criminals commie, we capitalists, we charge $$ for the
injections. We give commies + Elizibeth Warren types special shots of
synthitic goo, their final medicine. [...MOUSER...]

[Hants Wiggins]

Sergio wrote:

>> so you capitalists are thinking, knowingly the evolution worked on the
>> human immune system for millions of years, yet big capitalist pharma is
>> trying to convince you that's wrong, by lethally injecting toxic crap
>> directly into your blood circuitry, bypassing all natural evolved
>> defence barriers. But the immune systems includes those barriers. What
>> can you say in your defence? You capitalists are criminals.
>>
>>
> we not criminals commie, we capitalists, we charge $$ for the
> injections. We give commies + Elizibeth Warren types special shots of
> synthitic goo, their final medicine. [...MOUSER...]

the bitch is a big capitalist with shares in big pharma industry. You
can't make shit white, just by saying the capitalists are communists. You
are a lying bitch.

[Sergio]

Elizibeth Warren is your virtual mother, and knows what is good for you.
She has no white guilt, cause shes native american indian.
Just send her your money, She will redistribut it to her causes, just
like a true commie socialist rat bastard.

[Timothy Golden]

Communism and Capitalism are labor models. In case you hadn't noticed Machines do all the heavy lifting now.
It is the machines that caused this conflict and it is the machines that will end this conflict.
Technology reigns supreme.
But for free energy... and this is what the communists and the capitalists harvest of the human race.
As individuals to practice self sufficiency will always be the ideal form.
It is healthier and happier.
No killing; no throwing wrenches into the other's gears; no lies or propaganda; just good knowledge and advice on how to do things better, and occasionally too some bad advice worth calling somebody on. Then too the discovery is such a sweet process to share. As mathematicians isn't that what we do here on USENET? Who would like to hold this medium down? Surely not we ourselves? Well in human behavior the acronym
shooting myself in the foot
does seem to operate.
I believe I did just fracture my sternum about a week ago and it is only by aggravating it that I can detect it. Some will drive onward, possibly strengthening their bone structure in the process if knitting can be achieved. Hindsight is prototypical.

[Brice Leclaire]

Timothy Golden wrote:

>> > we not criminals commie, we capitalists, we charge $$ for the
>> > injections. We give commies + Elizibeth Warren types special shots of
>> > synthitic goo, their final medicine. [...MOUSER...]
>> the bitch is a big capitalist with shares in big pharma industry. You
>> can't make shit white, just by saying the capitalists are communists.
>> You are a lying bitch.
>
> Communism and Capitalism are labor models. In case you hadn't noticed
> Machines do all the heavy lifting now.

No, it's not. You can't compare and put capitalism together wit
communism. Because the capitalism is at the *bottom_of_the_dirt*. It
cannot fall lower. Which gives a touch of "stability" and "works" to the
morons. Only because it cannot *fall_lower*.

And NO. those are ways of life, ownership of the planet, for of
governance and the absence of it. See also Anarchism.

[Timothy Golden]

On Wednesday, March 3, 2021 at 12:42:35 PM UTC-5, Peter wrote:
> Timothy Golden wrote:
> > On Wednesday, February 17, 2021 at 3:55:10 PM UTC-5, Peter wrote:
> >> Timothy Golden wrote:
> >>> On Wednesday, February 17, 2021 at 2:46:32 PM UTC-5, Peter wrote:
> >>>> Timothy Golden wrote:
> >>>>> [...] So today I've gotten myself wondering: If set theory is
> >>>>> granted inherent order then what in mathematics gets obviated?
> >>>> In set theory an obvious way of defining an order is x < y iff x in
> >>>> y That "in" is the stylized epsilon read as "is an element of". It
> >>>> fails to have some of the properties that one might want of an
> >>>> order. E.g. trichotomy (that's "just one of x < y, x = y, y < x is
> >>>> true") fails.
> >>>>
> >>>> Another possibility is x < y iff x propersubset y but trichotomy
> >>>> still fails.
> >>>>
> >>>> Among von Neumann ordinals, x in y and x propersubset y coincide
> >>>> and x < y is defined to be either. Trichotomy does then hold.

> > Yes, it is problematic. The problem is that you've spent more information describing the unordered set than you would spend to describe the ordered set

> Only because you're too thick to get these elementary facts: (i) sets
> are unordered, (ii) language is ordered.

But this really is quite pertinent. It is so clear that our language does already use set theory in its ordered form particularly as language, and as formal language e.g. with dictionary lookups possible. A dictionary poses its own challenges to set theory, and it is there that one could argue that serious agreed upon elements are in use. If I wish to discuss a tarbuncle with you I should take some care.

The notion of arriving at an elemental level takes far broader meaning such that physicists' ears will prick up at that language. Yet this meaning is greatly diminished with the mathematicians version of 'element'. Lo and behold I find that this is a weak point that progressively weakens mathematics e.g. the binary operator and abstract algebra. If anyone should see this chain of thought, Peter, it is you.

For the mathematician it seems that elements are trivium; to be thrown around, created, and deleted at will. These same mathematicians are supposedly operating at a logical level that exceeds all other specialties. Their strictness and correctness is so good that ideas remain four hundred years after their creation with little to no further development, while such developments sit beneath the noses of millions within this sect.

If I explain to you that the behavior
- 1 + 1 = 0
does have other forms such as
- 1 + 1 * 1 = 0
so that a family of such systems is formed then clearly we are engaged in a rudimentary form
s x
where s is sign and x is magnitude. This product of unique types does not operate and so the form is stable. Within the realm there does exist a
MU : - 1 ( Minus Unity )
and likewise there is as well a
MU' = MU ^ (n-1) (where n is the signature of the system)
Is it possible that the grand conjugation does make use of these two? Both can cover the space nicely. I only recently have come to regard MU's prime as relevant, and from a perspective of symmetry it sadly does land us flat in the plane again, yet these values are not at all planar in their construction. Binary notions were to be gone in polysign; replaced by trinary, quaternary, and so on. The purist in me can still have that I suppose. Mathematics at some level is all about trickery isn't in? Perhaps this explains sci.math in its best context.

> > . Let's presume that we are not in any Cartesian product space as you've suggested earlier. We are discussing one set S1:
> > S1 = { w, x, y, z }
> > though the meaning of these 'elements' is ill defined. Certainly as belated letters of the English alphabet they will pass as authentic elements. Clearly under this interpretation they are not at all a complete set. Some sets do have rather great importance such as the real numbers, for instance, and admittedly they do not take this simplistic notation. Clearly we are settled into a discrete version here. Well, well, we settle for a discrete representation of every concrete value in the reals as well, e.g. 1.2345. This causes yet another conflagration since the elements are actually:
> > D10 = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
> > and so a discussion on what exactly is elemental ensues, with minor burns only to these digits which incidentally we all operate on as an unstated assumption. In hindsight all of our construction here is composed of combinations of these elemental glyphs. These are not regarded as Cartesian in nature, though arguably a 100 character document could be treated as a 100 dimensional discrete space. In fact when we find errors in typing it exposes that we benefit by not completely filling out that space. For systems like the real numbers we save ourselves quite a lot of time by not asking our students to scribe out values on increments of 0.0001 up to unity. The seemingly futile nature of the concrete form is alleviated by the elemental value 'a' and some neat tricks do develop there, but none of them obviate the usage of concrete values. Clearly such a set carries order, as do most sets, and to insist on disordering a system in order to fully declare it a set is foolhardy IMO.
> >
> > Under a structured thought perspective we ought to build more complicated things from simpler things. At some point we hope that we achieve such a basic representation as to name that system a basis. At some level we all are in search of the basis. As primates who came down from the tree branches many generations ago we must admit that we are engaged in a progression; a progression from naught which has taken many branches and has accumulated a tremendous pile of informatic content as we see on the internet or in the stacks of the college library. There are fundamental struggles and really lockups as the race condition of those fixated on infinity expose.
> >
> > If a computer compiler were told of a set of values in say an enumeration, it could go through those values one by one and if it found a match it could provide the functionality that enumerations allow for, typically in a switch(a) statement. However to tell that compiler to disorder an enumeration cannot possibly be a meaningful step.
> > This is clearly the problem with your language. It is only by convention of contorted humans whose mimicry responses are guaranteed by their social animal form (with linguistic mimicry to boot) that your language is acceptable. There is no compiler level integrity in the history of mathematics. We have now entered the computer age; an age where a compiler error is not something that we fight with. Control theory within a client / server methodology likewise inverts what appears to place the server as a high value asset. And yet the bifurcation is only meaningful in its duplicity. In reality the server side is generally the easy side of things. Too much complexity there will be sure to bungle things up; as in ftp, whereas http did achieve utter simplicity.
> >
> > In that set theory is to be fundamental in nature it would seem that a quagmire does ensue when you issue the requirement that a set you've just passed in an orderly fashion have most of its information removed. I don't really know that there is that much information left in the elements you've passed other than their order. As tokens go, they are merely tokens in an even playing field via the set status. To say, shuffle them at reception such that the sender has no idea how the receiver keeps them cannot be a wise choice within communication theory. Here I am holding by this idea that information theory could be in conflict with accepted set theory. Yes, we are securing this perspective.
> >
> --

> When, once, reference was made to a statesman universally
> recognized, to induce him to a judgment, he replied: "My situation is
> so different that it is not for me to piss and lament".
> Tim on Peter's life

[zelos...@gmail.com]

torsdag 11 februari 2021 kl. 17:37:15 UTC+1 skrev timba...@gmail.com:
> That's a bit overly specific, but the idea is present. To what degree does the bracket notation inherently impose order on a set, and then is elementhood all that has been declared? Clearly we do not list our alphabet that we speak with here arbitrarily, and every typo that I make whether admited or not as some cleaver goof has a correction listed somewhere in an orderly fashion. Is it only arbitrary that my alphabet is
> { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }
> and is this the alphabet that set theory is communicated from? Is this then not actually a set? And is the order merely happenstance? How strange that such a computationally integral concept could go unapplied when it is clearly readily available.
>
> I could see a cloud type of set theory whereby the elements are randomly arranged with some space between them enclosed in a circle, which certainly does go on diagrammatically in set theory when the intersection of two sets and the union of two sets are explained, though rarely do those notations actually carry serious elements. It so happens that another fairly serious 'set' of elements

> { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

> exist and that their order is entirely meaningful. Indeed I think we could have some trouble if I were communicating with the set
> { 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
> wouldn't we?
>
> Would it then be that
> 1 + 1 = 3
> is so for me but not for you?
> Clearly then someone ought to disambiguate.
> Yet it seems that the set theorists don't care.
> WTFIGOH?

when used for sets, order never matters.

[Timothy Golden]

It is a wonderfully short and accurate statement that does in fact deserve scrutiny. In response and in short I would argue that:

No simple set can be propagated without order.

This term 'propagate' is not really meant to be tricky. 'communicate' does fit, and communication is a form of propagation. Within relativity theory for instance if we are not able to propagate measurements from one place to another than no actual observable effect can be claimed. It is the usage of an observer at A, and an observer at another position B, and the comparison of their observations, including through the usage of a propagatable measuring rods, timing devices, etc., that makes the system definable. Without order you will never be able to define a set. Indeed the very notation
{ }
whose near equivalent
( )
or
[ ]
do in fact imply order. A list is promised to be enclosed between those marks and they (the marks) are regarde as a containent mechanism.

[Sergio]

<snip crap>



nothing...

[Gus Gassmann]

Order never matters for sets. {red, green, blue} is the same set as {red, blue, green}. Neither form implies an order on the elements, or a value statement, and certainly not an addition. If you want a set to have structure, you have to define it. And yes, you could define the set {1, 3, 2} and define addition on it in such a way that 1 + 3 = 2. But you'd have to communicate that fact together with the elements of your set.

[Timothy Golden]

The set {red, green, blue} is ordered. To claim that it is not is a falsifiable statement. This language is in its simplest terms; right where set theory belongs. And also then too we must ask what is this great chasm that occurs when we allow sets inherent order? Why would so many insist on such a shuffling of the deck? So as to maintain some sense of surprise? Well, surprise! Compilers don't like you and your old set theory any more. In fact the modern computer cannot possibly represent that which you claim to be a serious concept. Rather: upon implementing the procedures necessary to accommodate your ridiculous definition you will have a rather large and completely unnecessary pile of spaghetti. What will remain under the simple definition will likely take up less than ten percent of the necessary code. Possibly a one percent depending upon how heavily you will rely upon the random ordering of set elements; nay not even this; it is the utter disorder that will deny any elemental representation. This is about how bad you will have it. I suppose we can prototype some functions or something and begin the spaghettification.

[FromTheRafters]

What relation?

[mitchr...@gmail.com]

Those two sets have parity...

[Timothy Golden]

On Saturday, March 20, 2021 at 1:51:16 PM UTC-4, mitchr...@gmail.com wrote:
> Those two sets have parity...

Hey, this is a great thought Mitch. The parity sets; n factorial. You had better list them all out gas man. So let's see to declare a set of three elements will require the usage of, cheeshe, quite a lot of space depending on how many notation marks you let in. three factorial without any structure and, yeah, we all see how it goes when you get into large lots of elements. You know, tennis has sets too.

[Sergio]

ahh.....

[zelos...@gmail.com]

Sets are by definition orderless so tbe rest is ireelevant.

[Timothy Golden]

The trouble is that to implement this order-less requirement is actually a huge amount of work versus the ordered system. In effect this form of communication here is not commensurate with set theory under it's fundamental basis.

An instance of an orderless set theory would be a bag with tokens in it. Those tokens would be the elements of the set. They should have the same weight and shape; kind of like scrabble letters. Let's say you are developing your set definition; you're cutting little bits of wood up, planing them down, and striking their surface with ink, using the letters that you see here; our meek alphabet. Wow, this is really scrabble-like now. All is fair and good, but you being the definer of this set opt to break away and form of a new letter; the upside down 'v', not to be confused with the traditional 'n'. Fine and good, but you don't like the first one that you made, and you already deposited it into the bag. So you empty the bag out and scan every tile for that one to extract it and replace it with your second vesion. This is the operational mode of reading tiles out of this bag. They are well contained, but the efficiency with which they can be worked is abysmal. This is the unordered set theory and it will actually then under these conditions enter into rather a lot of random analysis; something completely overlooked in ordinary primitive set theory.

This is not an entirely bad piece of analysis and I'll admit that from my OP here I was against this thinking, yet here we do see quite some correspondence with reality. In fact we witness tremendous redundancy as well, so a clever critic here might say:
"Just throw the second upside down 'v' in the bag. Everything will be fine."
And now we see that with redundancy the bag and its contents and its count could have nothing to do with the number of elements in the set. There will be a stage of interpretation, and in the case of a pre-upside-down-v trained mind the two new tiles will be separated out away from the others and in essence rejected, even though they were in the bag. Possibly even they will be turned upside down by this old mind. This is roughly the position we are in here.

We do in fact exist in a reality that exposes tremendous redundancy. Probabilistic studies allow for rather an extensive amount of results from the bell curve on into conditioned deviations that go far beyond my own taste; repulsive to many for our clockwork training with one right answer to every problem. Training and habituation are possibly our greatest problem; our blessed curse. We propagate these strict interpretations generation to generation as if they were a religion... The human mind and its arithmetic core seem to be anal-retentive. Certainly the regurgitated state in which we exist does conflict with the notion of purity of the subjects at hand. Ideally we would come at these problems from a blank slate, and when we arrive again and again in the same position no matter how many mouse maze turns we make then we can claim a universal principle. I do not see that occurring here in set theory. As I see it we have a branch of interpretation, or two or three even, and lo and behold the most troubling one is the status quo IMO. No Zermelo-Frankel here. We are at the level of set construction here. This in its traditional form as:
S3 = { men, grass, earth }
and is this valid? The very looseness of the standard and its ease of allowing anything in as elemental really lacks seriousness. And of all things to claim that S3 lacks order is directly falsifiable by its definition. That none here can bight on this truth seems deeply retarded.

[zelos...@gmail.com]

sets are defined by the elements they contain, nothing else. That makes them orderless. So no need for the rest.

You got ordered pairs, ordered triplets, etc, but they are not sets (or if they are, very specifically designed sets)

[Timothy Golden]

On Thursday, February 11, 2021 at 11:37:15 AM UTC-5, Timothy Golden wrote:
> That's a bit overly specific, but the idea is present. To what degree does the bracket notation inherently impose order on a set, and then is elementhood all that has been declared? Clearly we do not list our alphabet that we speak with here arbitrarily, and every typo that I make whether admited or not as some cleaver goof has a correction listed somewhere in an orderly fashion. Is it only arbitrary that my alphabet is
> { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z }
> and is this the alphabet that set theory is communicated from? Is this then not actually a set? And is the order merely happenstance? How strange that such a computationally integral concept could go unapplied when it is clearly readily available.
>
> I could see a cloud type of set theory whereby the elements are randomly arranged with some space between them enclosed in a circle, which certainly does go on diagrammatically in set theory when the intersection of two sets and the union of two sets are explained, though rarely do those notations actually carry serious elements. It so happens that another fairly serious 'set' of elements
> { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
> exist and that their order is entirely meaningful. Indeed I think we could have some trouble if I were communicating with the set
> { 0, 1, 3, 2, 4, 5, 6, 7, 8, 9 }
> wouldn't we?
>
> Would it then be that
> 1 + 1 = 3
> is so for me but not for you?
> Clearly then someone ought to disambiguate.
> Yet it seems that the set theorists don't care.
> WTFIGOH?

There is a tendency to fail to cover any new ground. It can't hurt can it? I mean here we are; all here to discuss mathematics and what, we're all just supposed to regurgitate? This is considered ideal? Nay; now we must break away and simply answer no and discover any consequences of the ordered set uniqueness problem. If we cannot admit
{0,1} = {1,0}
then we must equivocate what the distinction is shan't we? Worst of all, as many arguments that I see lately do, to bottom out in the meaning of the elemental nature inevitably drives my analysis. As elements are the showcase definition within the set brackets the very first usage of these discrete beings? In this regard they are primitives, and here is how and why they cannot sway from their first definition. They need only be defined once, and with the bracket notation they inherently carry order. A set theorist who wishes to deny this ought then to do away with all of bracket notation. This then would ensue onto the Cartesian product; onto ordered notations in use throughout and often enough the source of disinformation. Many a time the ellipsis is included inside of the brackets. Possibly the correction lays in the fact that a family of sets exists and so as much as we like the natural numbers their antecedents include:
{0},{0,1},{0,1,2},{0,1,2,3}, ...
and this then disambiguates the situation. By the time we can count to nine we can count to three, yeah?

[zelos...@gmail.com]

There is a difference between creating new things where it does matter and just spouting shite. It is like the abstract algebra where you were too stupid to understand the difference between notation and actual construction.

In sets, order does not matter, because they are defined by content, not order.

That's the end there. If you want order to matter, you got filters/sequences for that, have fun there.

[Jackie Pysczynski]

Timothy Golden wrote:

> There is a tendency to fail to cover any new ground. It can't hurt can
> it? I mean here we are; all here to discuss mathematics and what, we're
> all just supposed to regurgitate? This is considered ideal? Nay; now we
> must break away and simply answer no and discover any consequences of
> the ordered set uniqueness problem. If we cannot admit
> {0,1} = {1,0}

https://committees.parliament.uk/writtenevidence/9253/html/

Our analysis under 3 establishes two parity arguments:

If Covid-19 ‘lockdown’ measures are compatible with human rights law,
then it is arguable that compulsory vaccination is too (lockdown parity
argument);
If compulsory medical treatment under mental health law for personal
and public protection purposes is compatible with human rights law, then
it is arguable that compulsory vaccination is too (mental health parity
argument).

Our chief conclusion is that, as and when a vaccine becomes available at
scale, the Government should give serious consideration to compulsory
immunisation as a means of reducing the impacts of Covid-19. There is an
arguable case for the compatibility of compulsory vaccination with human
rights law.

[Sergio]

so, why does this happen to you ?

[Jackie Pysczynski]

Sergio wrote:

>> definition. That none here can bight on this truth seems deeply
>> retarded.
>>
> so, why does this happen to you ?

Sorry to interrupt you, just a little song I want to share with you guys, traa lala lala.., wake the fuck up, traa lala lala..

List of largest List of largest *bourgeoisie_capitalist* pharmaceutical settlements pharmaceutical settlements
https://en.wikipedia.org/wiki/List_of_largest_pharmaceutical_settlements

2012 GlaxoSmithKline[1][6] $3 billion ($1B criminal, $2B civil) Criminal: Off-label promotion, failure to disclose safety data.
Civil: paying kickbacks to physicians, making false and misleading statements concerning the safety of Avandia, reporting false best prices and underpaying rebates owed under the Medicaid Drug Rebate Program Avandia (not providing safety data), Wellbutrin, Paxil (promotion of paediatric use), Advair, Lamictal, Zofran, Imitrex, Lotronex, Flovent, Valtrex False Claims Act, FDCA
2009 Pfizer[2] $2.3 billion Off-label promotion, kickbacks Bextra, Geodon, Zyvox, Lyrica False Claims Act, FDCA
2013 Johnson & Johnson[7] $2.2 billion Off-label promotion, kickbacks Risperdal, Invega, Nesiritide False Claims Act, FDCA
2012 Abbott Laboratories[8] $1.5 billion Off-label promotion Depakote False Claims Act, FDCA
2009 Eli Lilly[9] $1.4 billion Off-label promotion Zyprexa False Claims Act, FDCA
2001 TAP Pharmaceutical Products[10] $875 million Medicare fraud, kickbacks Lupron False Claims Act, Prescription Drug Marketing Act
2012 Amgen[11] $762 million Off-label promotion, kickbacks Aranesp False Claims Act, FDCA
2010 GlaxoSmithKline[12] $750 million Poor manufacturing practices Kytril, Bactroban, Paxil CR, Avandamet False Claims Act, FDCA
2005 Serono[13] $704 million Off-label promotion, kickbacks, monopolistic practices Serostim False Claims Act
2008 Merck[14] $650 million Medicare fraud, kickbacks Zocor, Vioxx, Pepsid False Claims Act, Medicaid Rebate Statute
2007 Purdue Pharma[15] $601 million Off-label promotion Oxycontin False Claims Act
2010 Allergan[16] $600 million Off-label promotion Botox False Claims Act, FDCA
2010 AstraZeneca[17] $520 million Off-label promotion, kickbacks Seroquel False Claims Act
2007 Bristol-Myers Squibb[18] $515 million Off-label promotion, kickbacks, Medicare fraud Abilify, Serzone False Claims Act, FDCA
2002 Schering-Plough[19] $500 million Poor manufacturing practices Claritin FDA Current Good Manufacturing Practices
2006 Mylan[20] $465 million Misclassification under the Medicaid Drug Rebate Program EpiPen (epinephrine) False Claims Act
2006 Schering-Plough[21] $435 million Off-label promotion, kickbacks, Medicare fraud Temodar, Intron A, K-Dur, Claritin RediTabs False Claims Act, FDCA
2004[22] Pfizer $430 million Off-label promotion Neurontin False Claims Act, FDCA
2008 Cephalon[23] $425 million Off-label promotion[23] Actiq, Gabitril, Provigil False Claims Act, FDCA
2010 Novartis[24] $423 million Off-label promotion, kickbacks Trileptal False Claims Act, FDCA
2003 AstraZeneca[25] $355 million Medicare fraud Zoladex Prescription Drug Marketing Act
2004 Schering-Plough[26] $345 million Medicare fraud, kickbacks Claritin False Claims Act, Anti-Kickback Statute

[michael Rodriguez]

(subthread)
w = (-3 # +5 # *11 # @23)
reciprocalOf(w) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
w·reciprocalOf(w) = -1 # +1 @ *1 # @2 = @1
path :
w = -a # +b # *c # @d
where # is addition symbol in p4
example with -3 # +5 # *11 # @23
1/w = 1/(-a # +b # *c # @d)
w~= -'a # +b # *'c # @d
where s' m <-> aditiveInverseOf( sm )
1/w = (1/w)(w~/w~) = w~/(ww~)
w~/(ww~) = (-'a # +b # *'c # @d ) / ( ( -a # +b # *c # @d) (-'a # +b # *'c # @d) )
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( ( -3 # +5 # *11 # @23)(-'3 # +5 # *'11 # @23) )
w~/(ww~) = (-'a # +b # *'c # @d ) / (+'a^2 # @b^2 # +'c^2 # @d^2 # @'2ac # +2bd )
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( +'9 # @25 # +'121 # @529 # @'66 # +230 )
Note that is enough with express the statement just with the signs @, + ,@' and +'
and is not necessary convert if remain symbol @' and +'...
w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( @480 # +100 )
Now, we complete to make difference of squares in the denominator , but
one must be careful to complete it towards the greatest number, not the smallest
as (x # y)(x # y') if x>y, or as (x # y)(x' # y) if x<y
..in this case we keep @480 invariable in the difference of squares, since it s the greatest
(w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( (@480 # +100)(@480 # +'100) )
(w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( @228144 )
(w~z)/(ww~z)=(-'1464 # +2440 #*'5368 # @11224 #*300 #@'500 # -1100 #+'2300)/@228144
(... a brief pause to drink some green juice...)
(w~z)/(ww~z) = ( -5068 # +5572 # *364 # @16156 )/@228144
hammering the neutral-signed terms upwards
(w~z)/(ww~z) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
(w~z)/(ww~z) = reciprocalOf( w )

Maybe one could tweak a bit the internal mechanics of symbols to smoothly allow "embedded signs"... cheers, lalo

[Sergio]

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[Timothy Golden]

On Monday, March 29, 2021 at 4:30:22 PM UTC-4, michael Rodriguez wrote:
> (subthread)
> w = (-3 # +5 # *11 # @23)

This could just read:
w = - 3 + 5 * 11 @ 23
but it also needs to be stated what domain you are in. If this is a P4 value, and the #'s gave that away, then it should simply be noted.
This then means that we could as well have( in P4 )
w = + 2 * 8 @ 20
but possibly in performing the reciprocal mechanics having nonzero values is useful. Strangest part though is that the reciprocals should all work out to be the same.

> reciprocalOf(w) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
> w·reciprocalOf(w) = -1 # +1 @ *1 # @2 = @1

I have not verified this yet.

> path :
> w = -a # +b # *c # @d
> where # is addition symbol in p4
> example with -3 # +5 # *11 # @23
> 1/w = 1/(-a # +b # *c # @d)
> w~= -'a # +b # *'c # @d
> where s' m <-> aditiveInverseOf( sm )

Hmmmm....

> 1/w = (1/w)(w~/w~) = w~/(ww~)

Wow. You have a conjugate form?

> w~/(ww~) = (-'a # +b # *'c # @d ) / ( ( -a # +b # *c # @d) (-'a # +b # *'c # @d) )
> w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( ( -3 # +5 # *11 # @23)(-'3 # +5 # *'11 # @23) )
> w~/(ww~) = (-'a # +b # *'c # @d ) / (+'a^2 # @b^2 # +'c^2 # @d^2 # @'2ac # +2bd )
> w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( +'9 # @25 # +'121 # @529 # @'66 # +230 )
> Note that is enough with express the statement just with the signs @, + ,@' and +'
> and is not necessary convert if remain symbol @' and +'...
> w~/(ww~) = (-'3 # +5 # *'11 # @23) / ( @480 # +100 )
> Now, we complete to make difference of squares in the denominator , but
> one must be careful to complete it towards the greatest number, not the smallest
> as (x # y)(x # y') if x>y, or as (x # y)(x' # y) if x<y
> ..in this case we keep @480 invariable in the difference of squares, since it s the greatest
> (w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( (@480 # +100)(@480 # +'100) )
> (w~z)/(ww~z) = ( (-'3 # +5 # *'11 # @23)(@480 # +'100) ) / ( @228144 )
> (w~z)/(ww~z)=(-'1464 # +2440 #*'5368 # @11224 #*300 #@'500 # -1100 #+'2300)/@228144
> (... a brief pause to drink some green juice...)

I hope it wasn't peyote...

> (w~z)/(ww~z) = ( -5068 # +5572 # *364 # @16156 )/@228144
> hammering the neutral-signed terms upwards
> (w~z)/(ww~z) = -(5068/228144) # +(5572/228144) # *(364/228144) # @16156/228144)
> (w~z)/(ww~z) = reciprocalOf( w )
>
> Maybe one could tweak a bit the internal mechanics of symbols to smoothly allow "embedded signs"... cheers, lalo

Well, well. You've done it again.
I guess I'll try to go through a rudimentary instance and maybe you could hold my hand if I make a boo-boo.
In P4, let z1 = * 3.
Then ~z1 = @ 3 - 3 + 3.
( z1 )( ~ z1) = * 9 @ 9 - 9
1 / z1 = ( @ 3 - 3 + 3 ) / ( * 9 @ 9 - 9 )

Well, I could have just had
1 / z1 = - 0.3333
from the get-go, and it might be in there somehow, but I guess I am stuck.

Anyway, I hope you are correct and that it is general to Pn too. That would be very great news.
Spring here is roaring in like a lion, and yesterday we had our biggest roar yet.

[Gus Gassmann]

On Friday, 19 March 2021 at 20:30:30 UTC-3, timba...@gmail.com wrote:
> The set {red, green, blue} is ordered. To claim that it is not is a falsifiable statement.

[...]
Go ahead, falsify this statement.

[FromTheRafters]

He won't be able to do that, but you knew that already.

That set is not ordered, but can be considered to be in a natural order
by increasing frequency of the associated light waves if one wants to
impose an order on it, but by that set notation alone it is order
independent.

The set {green, blue, red} is the same set.

[Timothy Golden]

The work involved in destroying the order of the set
{ red, green, blue }
is considerable. I find it interesting how inflexible minds are that have been trained on mathematics.

There must be a philosophy of covering the ground. Especially when some fundamental choice exists, and the options can be covered, they ought to be covered. The option to allow the set definition
{ e1, e2, e3 }
to be ordered is obvious, and this merely as a bifurcated system cannot be far off from formalization here. Yet which is the more primitive form: now we have a contentious problem and again we must state that mathematicians of yore had no compiler level of integrity to operate from.
What appears simpler is not always so.

Again also I must stress the notion of elementhood as something so primitive, and yet it is our very linguistics getting in the way, for we know which is more primitive to humans. We learn our first language out of thin air and so it should be true as well of mathematics. When a child learns their abc's and the set theorist has something to say about it, it goes something like this:
"That's just fine Johnny. When the disonance in class rises as you all sing it try and stay focused on your version. Yell it if you must."

[Gus Gassmann]

As FromTheRafters said, you can't prove that { red, green, blue } forces an order on the set. (And, yes, I knew that you wouldn't be able.) All you have is wishful thinking. Note how you yourself call the order an "option". Nothing more. I didn't sign up for that option; I don't need it.

[Timothy Golden]

I don't believe that this is a matter of proof. This is merely a matter of construction. If anything the natural order of a set defined with the bracket notation is obvious and trivial. I understand that the tradition is different than what I am speaking of. This is not a realm in which we have to settle for one or the other. At least not initially. To spend our days regurgitating what has already been is hardly a position worth holding. Investigating options and weighing the differences I don't feel as if the standard theory is so strong. What exactly it means to maintain a series of elements without any order is greatly problematic. Disorder is not something that mathematics really does well. How probability theory can be so far away from set theory under this interpretation; it should not be so. Possibly we will witness the entrance of random variables earlier if we take set disorder more seriously. I'm open to all sorts of side effects.

[zelos...@gmail.com]

We have defined it not to be ordered in sets because sets are defined by their elements and nothing else. From this we we can create ordered n-tuplets which is what you want.

[Gus Gassmann]

On Tuesday, 30 March 2021 at 20:56:47 UTC-3, timba...@gmail.com wrote:
> On Tuesday, March 30, 2021 at 1:27:56 PM UTC-4, Gus Gassmann wrote:
> > On Tuesday, 30 March 2021 at 14:03:42 UTC-3, timba...@gmail.com wrote:
> > > On Tuesday, March 30, 2021 at 9:18:35 AM UTC-4, Gus Gassmann wrote:
> > > > On Friday, 19 March 2021 at 20:30:30 UTC-3, timba...@gmail.com wrote:
> > > > > The set {red, green, blue} is ordered. To claim that it is not is a falsifiable statement.
> > > > [...]
> > > > Go ahead, falsify this statement.
> > > The work involved in destroying the order of the set
> > > { red, green, blue }
> > > is considerable. I find it interesting how inflexible minds are that have been trained on mathematics.
> > >
> > > There must be a philosophy of covering the ground. Especially when some fundamental choice exists, and the options can be covered, they ought to be covered. The option to allow the set definition
> > > { e1, e2, e3 }
> > > to be ordered is obvious, and this merely as a bifurcated system cannot be far off from formalization here. Yet which is the more primitive form: now we have a contentious problem and again we must state that mathematicians of yore had no compiler level of integrity to operate from.
> > > What appears simpler is not always so.
> > >
> > > Again also I must stress the notion of elementhood as something so primitive, and yet it is our very linguistics getting in the way, for we know which is more primitive to humans. We learn our first language out of thin air and so it should be true as well of mathematics. When a child learns their abc's and the set theorist has something to say about it, it goes something like this:
> > > "That's just fine Johnny. When the disonance in class rises as you all sing it try and stay focused on your version. Yell it if you must."
> > As FromTheRafters said, you can't prove that { red, green, blue } forces an order on the set. (And, yes, I knew that you wouldn't be able.) All you have is wishful thinking. Note how you yourself call the order an "option". Nothing more. I didn't sign up for that option; I don't need it.
> I don't believe that this is a matter of proof. This is merely a matter of construction.

It is distinctly *not* a matter of construction. You can construct sets by set operators such as union and intersection. Suppose you have the two sets {red, green, blue} and {red, blue, green}. I guess you would treat them as different sets, but what would you think is {red, green, blue} intersected with {red, blue, green}?

Or take the two sets {1, 2, 3} and {5, 4, 3}. What is their union?

The only way to make sense of the set operations is to declare sets as unordered. If you want to operate on ordered sets, you (Tim Golden) will have to work out what the order should be.

[...]

[Timothy Golden]

I appreciate your non-assaultive response, but in it do lay some more details worth turning over. We know of the bracket notation
S = { e1, e2, e3, e4, ... en }
but really we know that only a few sets can be well stated this way. For instance
S[Letters = { a, b, c, d, e, f, ..., x, y, z }
S[Numbers] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 }
S[Binary] = { 0, 1 }
S[Hexadecimal] = { 0, 1, 2, 3, ..., 8, 9, A, B, C, D, E, F }
are all actual instances of useful discrete sets. What we find though is that their usage and nature is only elemental in a partial sense. It is their reuse in sequential combinations which then establish the representations that are generally useful. That these discrete forms take on modulo usage within representations (as our native tongue requires) denies any basic value to their elemental status. Having picked apart our words down to these letters we will find no meaning whatsoever. We will find statistical qualities such as a high frequency of 't' and 'e' yet this can do little to assign any meaning other than to identify the language in use as English.

As we get into mathematics more, we see that real analysis is a subject which attempts a purity above S[Numbers]. They engage with the value 'a' as a first instance and attempt to operate on a list of axioms as their basis, so in this way your statement is false: not all sets are defined via the bracket notation. Elementhood in the real numbers has gone to another form. The notion that we must first build the real numbers without any sense of order and then impose order on them all is about as senseless a pursuit I believe as one can muster.

[Timothy Golden]

Oh, yes, you are now getting into it Gus. I think the notion of plurality of a unique element within a set has to be breached as well. For instance within the reals let's say that x is 2.0. Now if we introduce a y and want it to take the value 2.0 shall we have to check in with the x first? Ought we to have written that very first set instance as
S = { red, red, red, ..., blue, blue, blue, ..., green, green, green, ... } ?
Oh and the Cantorians will insist on the reorder to:
S = { red, blue, green, red, blue, green, red, blue, green, ... } ;
yes, this latter must be the superior notation. Elementhood as Robbin Hood would have it. Plenty to go around for everybody.

[Timothy Golden]

And of course this identification of English has to be done from the ordered set. From the insistence of the disordered set theory all that you will have is a count of letters, if even that. Possibly due to the intense lack of order within your set theory your own ability to even count elements will be nonexistent.

[Gus Gassmann]

I see nothing here where you even remotely address the questions I posed. I won't contribute further to this thread.

[Timothy Golden]

Well Gus, I didn't realize you has some grand plan going with your union there. We know that the answer to your question from within ordinary set theory is
{ 1, 2, 3, 4, 5 }
Now as you mention set operations making sense, Let's consider doing this union based on 1E6 elements in each of the source sets. Due to the disorder of the sets the operation will take quite some time to perform. Especially the insistence on the disordered medium of set theory would be very problematic mid way through your operation. You are bound to get bad results. It is not actually possible to do a clean union on truly disordered sets. The checker will have no means of enumeration. When the requirement that sets contain no order goes out, secretly in their back pocket, the mathematicians kept an order that they did not want to admit. This order was the initial definition. Clearly you will have to rely upon that order to perform the union.

Lastly though, the lack of seriousness of the elemental nature of set theory; something which arrives on ground tantamount to a physical basis; is overlooked so badly in all of this. Then we arrive at the seriousness of the real value; something which physicists work with; chemists and engineers work with; oh no, the mathematician says, I can assure you that they merely work with rational numbers. They think that close enough is good enough whereas we mathematicians play on a higher form. Our work is truly for the Queen.

We are led to believe that number is a sufficient basis for reality. We are taught that the Cartesian product is the way into general dimension. The difference between construction and representation is relevant here. When I construct the plane via
- 1.0 + 1.0 * 1.0 = 0
its nature is demanded no different than the real line is demanded by
- 1.0 + 1.0 = 0

The flimsy nature of the Cartesian product is understandable through this lens and the consequences do seem to resound throughout the subject.
It is a bear that many hunting parties have missed. Meanwhile it has been sitting under their noses for half a millennium.So what gives?

Polysign gives.
The revolution will not be televised.
https://www.youtube.com/watch?v=7ulE1AYhqTw
https://www.youtube.com/watch?v=QnJFhuOWgXg
The status quo position is a fraud sir.
I do understand that it is not so easy to break through.
I do understand why so many fail to vote in this supposedly democratic country.
(With provable rigged democratic party primaries in 2016 and 2020 in light of a democratic socialist nearing leadership)
I do understand as well why so many have a hard time in mathematics.
Those who do well simply are submissive followers.
They will practice their regurgitative skills onto others and propagate the status quo just as a tribe of monkeys will stand by their leader.
The assumption that we have escaped our animal nature helps establish mathematics as a religion.
We continue to bow to the greats of the subject. I obviously will not have such at my door.
Not if status quo power has anything to say about it.

We will still have our social structure without the almighty dollar.
Indeed the dollar is that cause of the collapse of our structure
And the digressive behavior that we impose on the rest of the world.
That dollar is getting less and less mighty by the year.
What we have done to VZ will come back to haunt us.
Oh, the list is long if you want the full list sir.
Embarrassingly long in both time and space.
I would like to have nothing to do with such a thing.
I would like to go down as fighting that thing.
That thing which most will submit to I choose to resist.
Oh, to be a wrench in the gears of cutthroat capitalism
just as we have thown so many wrenches into the gears of idealists around the world.
The big lie sir we have lived our entire lives now.
Well, it has failed anyway with or without my input.
That an uncorruptible form might exist;
We will have to try again you see?

[FromTheRafters]

Timothy Golden brought next idea :

Assuming it takes time to do a union. Why must it be so?

[Timothy Golden]

That is possibly a very deep question. If you do believe that set theory lays at the foundation of all then that becomes especially relevant I think.
Standard set theory is a fairly easy subject but it seems to lack seriousness.
Then too the set of real numbers will be confessed by virtually all to be a very key system to our understanding of reality.
The notion that real analysis is secured at its base by set theory could be taken as a structural flaw.
A basis is a very raw thing.
That the real numbers build out as a conglomerate in the ordinary teaching does not really help them from a structural point of view.
That they then get swept into the complex numbers likewise is not really something to be so proud of.
That someone would bother to fill in the holes of a discrete system in order to wind up in a continuous system is really not such a convincing plan of attack. The discrete system demands respect and the continuous system likewise demands respect. To blur them is a fraud.
Perhaps it is my engineer training, but the number of times that close enough is not good enough are far and few between.
I can happily confess that the amazing 64 bit machinery at my fingertips is performing rational operations.
Epsilon-Delta theory still applies. The proof of continuum lays there; not in the raw value.
Also its not as if I think programmers have it perfect either.
When we are caught having to declare:
long long long int x;
won't that say it all?
We are all caught in a process of accumulation.
It is coming time to wipe the slate clean.

[Sergio]

no, it shallow.

> If you do believe that set theory lays at the foundation of all then that becomes especially relevant I think.

if statement, wrong.

> Standard set theory is a fairly easy subject but it seems to lack seriousness.

your personal opinion.

> Then too the set of real numbers will be confessed by virtually all to be a very key system to our understanding of reality.

wrong. most do not know what a "set" is.

> The notion that real analysis is secured at its base by set theory could be taken as a structural flaw.

your notion is wrong.

> A basis is a very raw thing.

you BOT

[Gus Gassmann]

Not true. It could just as easily be {1, 2, 3, 5, 4}, ignoring the duplicates. *ORDER DOES NOT MATTER*.

> Now as you mention set operations making sense, Let's consider doing this union based on 1E6 elements in each of the source sets. Due to the disorder of the sets the operation will take quite some time to perform. Especially the insistence on the disordered medium of set theory would be very problematic mid way through your operation. You are bound to get bad results.

I have no clue what you mean by "bad results", and I doubt that you do, either. All I note is that you have admitted to being unable to find the union of two sets that contain a million elements each. That's pretty sad, actually.

> It is not actually possible to do a clean union on truly disordered sets.

WTF is a "clean union"?

> The checker will have no means of enumeration.

Who or what is the "checker", and what would be enumerated? There are clean and clear algorithms (in at most O(n^2) ops that will compute a union or an intersection of two finite sets.

> When the requirement that sets contain no order goes out, secretly in their back pocket, the mathematicians kept an order that they did not want to admit. This order was the initial definition. Clearly you will have to rely upon that order to perform the union.

Sure. Nobody is saying that you should consider every permutation of the elements before you can compute a union. But that sure as hell is not the same as a literal order, where 1 < 2 < 3 or, if the set is given as {1, 3, 2}, 1 < 3 < 2. In particular, I want to emphasize that {1, 2, 3} and {1, 3, 2} represent the same set.

[...]

[Timothy Golden]

Well Sergio and Gus the gas man do have some tender under belly. Weak responses both. Here though I find a flaw.

The gas man says:
"There are clean and clear algorithms (in at most O(n^2) ops that will compute a union or an intersection of two finite sets."

and what he fails to confess is that these very algorithms will rely upon the orderly enumeration of the elements of these sets.
But he claims that his sets lack order. This is a conflict.

At best on disordered sets only a probablility of accurate union will be arrived at under the disordered method.
Let's now take this to the next level and offer up a method of accessing an element of a disordered set:
const Element & DisorderedSet::GetElement()
{ // a disordered set will be required to return a random element of an ordered set.
// there is no other way to code this as far as I can tell. (AFAICT)
return OrderedSet.GetElement( OrderedSet.RandomElement(this));
}

Honestly I cannot guarantee that this code will compile but I do believe that the idea of the disordered set pre-existing the ordered set is a clear fallacy from the standpoint of ordinary logic. That you have fallen into your own trap here is a very good sticking point. Do not back out. Do not move one iota, for you have the jaws upon you now. Await help from some higher up authority to get you out of your predicament.

[Man From a city with name Viljandi]

Set is defined of containing elements.

[FromTheRafters]

Timothy Golden wrote :

> Well Sergio and Gus the gas man do have some tender under belly. Weak
> responses both. Here though I find a flaw. The gas man says:
> "There are clean and clear algorithms (in at most O(n^2) ops that will
> compute a union or an intersection of two finite sets."

But you don't need an algorithm to encapsulate the *idea* of
intersection and/or union any more than you need an infinitely thin
pencil point to encapsulate the *idea* of a circle and/or a line.

Mathematics and computation are closely related but not the same thing.

[Timothy Golden]

I do in fact agree with your sentiment, yet the computability of such a thing as a set union does have to be taken seriously.
Particularly as we explore the meaninglessness of a set which lacks order.
Come now from the ceiling down to the floor.
Are you ever going to admit that the first thing you will do to perform your union is access the first element of your two sets and compare them?
Even as we consider the differences between the elements we will arrive in a sense of order above and beyond the problem of access.
You see how readily the disordered set falls apart at the seams.

At least I hope that you can explain how a human is to perform the set union so differently than the computer?
Yes, that is a badly phrased question, but still I think you could manage the grammar, Rafter.
Or is it that the idea is so good (standard set theory) that nobody ought ever to challenge it since it was laid down by the greats who came before us? This would be teetering on religion wouldn't it?

[Timothy Golden]

On Saturday, April 3, 2021 at 9:15:59 AM UTC-4, FromTheRafters wrote:

> Timothy Golden wrote :
> > Well Sergio and Gus the gas man do have some tender under belly. Weak
> > responses both. Here though I find a flaw. The gas man says:
> > "There are clean and clear algorithms (in at most O(n^2) ops that will
> > compute a union or an intersection of two finite sets."
> But you don't need an algorithm to encapsulate the *idea* of
> intersection and/or union any more than you need an infinitely thin
> pencil point to encapsulate the *idea* of a circle and/or a line.

And incidentally your point here on the thickness of a pencil point or line trace is a valid problem.

[FromTheRafters]

Timothy Golden presented the following explanation :

> On Saturday, April 3, 2021 at 9:15:59 AM UTC-4, FromTheRafters wrote:
>> Timothy Golden wrote :
>>> Well Sergio and Gus the gas man do have some tender under belly. Weak
>>> responses both. Here though I find a flaw. The gas man says:
>>> "There are clean and clear algorithms (in at most O(n^2) ops that will
>>> compute a union or an intersection of two finite sets."
>> But you don't need an algorithm to encapsulate the *idea* of
>> intersection and/or union any more than you need an infinitely thin
>> pencil point to encapsulate the *idea* of a circle and/or a line.
>>
>> Mathematics and computation are closely related but not the same thing.
>
> I do in fact agree with your sentiment, yet the computability of such a thing
> as a set union does have to be taken seriously. Particularly as we explore
> the meaninglessness of a set which lacks order. Come now from the ceiling
> down to the floor. Are you ever going to admit that the first thing you will
> do to perform your union is access the first element of your two sets and
> compare them?

Obtaining the elements of the elements only requires a layer of
un-nesting.

> Even as we consider the differences between the elements we
> will arrive in a sense of order above and beyond the problem of access. You
> see how readily the disordered set falls apart at the seams.

The axioms have to work for sets other than numbers too.

> At least I hope that you can explain how a human is to perform the set union
> so differently than the computer? Yes, that is a badly phrased question, but
> still I think you could manage the grammar, Rafter. Or is it that the idea is
> so good (standard set theory) that nobody ought ever to challenge it since it
> was laid down by the greats who came before us? This would be teetering on
> religion wouldn't it?

I'm not a math zealot, I just consider 'computable numbers' and
'constructable numbers' to be subsets of *numbers* which I generally
take to be real numbers which all exist just in case one needs to point
to one or a set of them as being the subject of discussion. Decimal
representation helps with labeling them. Taking the label as a
computation which must be completed in a finite time to "instantiate"
the number in question is wrong headed IMO -- it is just a
representation like the CFE is -- there is no need to complete the
ongoing computation since that computation is only the representation
of the number and not the number itself.

I'm not too keen on the idea of building a house of mathematics and
then trying to slide a foundation underneath it, but we always like to
break things down into smaller (atomic) pieces only to find reality has
a fractal nature and the more we look at the big and the small the more
we know about the unknown unknowns. In this case they seek ZFC set
theory and its underlying logic as the "best" fit so far for much of
mathematics.