Am I just confused or is everyone else?
Douglas
What's the problem with this infinity thing?
I - I = I.
Right?
Eg.
I have a 2 cars going in a straight line one in front of the
other. If the second car reaches the first car, you die.
They are twenty litres worth of fuel a part.
Okay, you:
Gain 1 life: The first car gets 1 litre of fuel and goes 1 litre of
fuel's worth forward. Now the cars are 21 litres worth of fuel a
part.
Lose 1 life: The second car gets 1 litre of fuel and goes 1 litre of
fuel's worth forward. Now the cars are 20 litres worth of fuel a
part again.
Lose 20 life: The second car gets 20 litre of fuel and goes 20 litres of
fuel's worth forward. Now the cars are 0 litres worth of fuel a part.
You die.
Gain Infinity life: The First car goes forward for ever.
You lose infinity life: The second car goes forward for ever.
The second car will never catch the first car. Right?
Is that a bad example? Why?
What's wrong with it?
Thanks,
Dug.
AlbertPark
do...@woozle.dialix.oz.au (Douglas) wrote:
>What's the problem with this infinity thing?
>
>I - I = I.
>
>Right?
but, I - I = I only if the first I is greater then the second. If the
first I equels the second I then I - I = zero. Of course, just for closer
sakes, if the second I is bigger then I - I = negative infinity.
Your example is for two equel infinities so the equation would equel zero.
An example of infinity minus infinity equels infinity is:
(set of all real numbers from one to infinity) - (the set of all integer
numbers from one to infinity) = infinity
Scott Gagon
In <57dms5$3...@nnrp1.farm.idt.net> AlbertPark <alp...@198.4.75.47>
writes:
>do...@woozle.dialix.oz.au (Douglas) wrote:
>>What's the problem with this infinity thing?
>>
>>I - I = I.
>>
>>Right?
>Depends. It might sound weird for anyone without some math background
>but, I - I = I only if the first I is greater then the second.
No. I - I does not equal *anything*. It's not a legal mathematical
expression. Also one infinity cannot be said to be greater than
another. Infinity is *NOT* a number, it has no real value and therefore
cannot be treated as one.
Practically, infinity shouldn't be used in play, instead substitute
some arbitrarily high number. Like I said, infinity is not a number,
therefore, X (in the case of a Fball or SoLife) cannot "equal" infinity
because X must equal some number and infinity isn't one.
Scott
ps: Whoever would have thought that 3 semesters of Calculus would
actually have a use in normal life??
Douglas
I got another one.
You life is represented as a road.
When you lose life, the car goes forward.
When you gain life, the car reverses.
When the car reaches the end of the road, you die.
Right?
You gain Infinite life: The car reverses until it is an Infinite
distance away.
You lose Infinite life: Will the car ever reach the end of the road?
MY answer? Probably not in this life time. But as things are ruled to
resolve really quickly, who knows?
Theory:
Explain please:
I + 1000 = ?
I + 199 = ?
I + I = ?
I * 2 = ?
I * 123 = ?
I * I = ?
I - 10 = ?
I - 1992 = ?
I - I = ? Okay the last one can be your oppinion if you like.
Where I is Infinity.
Justification would be nice as well.
George W. Bayles
Scott Gagon (scot...@ix.netcom.com) wrote:
[snip]
: Practically, infinity shouldn't be used in play, instead substitute
: some arbitrarily high number. Like I said, infinity is not a number,
No way. There isn't any arbritrarily high number that wouldn't create more
problems than using it "solved".
: therefore, X (in the case of a Fball or SoLife) cannot "equal" infinity
: because X must equal some number and infinity isn't one.
For any number you pick I could add one to it. You can't pick an arbritrary
stopping point and say "no more".
: Scott
David DeLaney
scot...@ix.netcom.com(Scott Gagon) writes:
>No. I - I does not equal *anything*. It's not a legal mathematical
>expression.
True, unless you define it more strictly.
>Also one infinity cannot be said to be greater than another.
False; Georg Cantor [yes, that's spelled correctly] proved otherwise many
decades ago. The infinity which counts the natural numbers is strictly
smaller than the infinity which counts the real numbers.
>Practically, infinity shouldn't be used in play,
But Magic is not always susceptible to practical considerations.
Dave
--
\/David DeLaney d...@panacea.phys.utk.edu "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK>
http://enigma.phys.utk.edu/~dbd/ - net.legends FAQ / I WUV you in all CAPS! --K.
Eric Taylor
Douglas (do...@woozle.dialix.oz.au) wrote:
: Is that a bad example? Why?
: What's wrong with it?
Well, first of all you have various types of infinities. There's
Aleph-null (for instance, the number of integers), there's c the
continuum, called Aleph-one, then Aleph-two etc.
However, normal math does not work on *any* infinite. You can not add
and subtract infinite numbers with normal math.
Consider this:
Infinity + 1 = Infinity Right? You add 1 to infinity,
it's still infinite.
Then if you subtract Infinity from both sides, you get
1 = 0
Ok, so normal math doesn't work, it's broken, then how do you treat
these numbers?
The math that you can do with infinities is by adding and subtracting
their cardinal (i.e. number of members of the set) numbers. That is,
you find some function which can count up the numbers and then if the
function is "one-to-one" then the infinity is less than or equal to the
other one where if they count "onto" then the infinity is greater than
or equal to.
For example, you have the evens, 2, 4, 6, 8, etc. Now if you take the
integers, you can see that you can assign 1 to 2, assign 2 to 4 as the
2nd even, 3 to 6, etc. In this way, you can prove
cardinality(Infinity(odd numbers)) = cardinality(Infinity(even numbers))
How about the reals. It's easy to see that the integers are a subset
of the the irrationals so that. . .
cardinality(Infinity(reals)) >= cardinality(Infinity(integers))
With a little more work, you can prove the ">=" is actually a ">".
The large number generated by atog and enduring renewal is not
infinity. It is merely as large of a number as you like. The only
infinities so far are any one of the infinities generated by ivory
gargoyle-like interactions and all of these infinities are Aleph-null
infinities including infinite numbers of carrion-ed tokens made from an
infinite asmira with martin stromgald attacking. For these types of
infinities, in terms of cardinality,
Aleph-null + Aleph-null = Aleph-null
Aleph-null - Aleph-null = undefined
Be careful when people talk about adding and subtracting infinities.
If he's a mathematician, he is talking only about the cardinal
numbers. However, a physicists or an engineer has no problem using
infinities alongside normal numbers. He just types in the biggest
number in his pocket calculator and calls it infinite.
Personally, I think the infinities generated by magic are wonderful.
What other game requires application of Cantor's theories as a *side
effect*?
--- edt
David DeLaney
These equal I+1000 and I+199, respectively; you count to I, then count that many
more finite steps.
>I + I = ?
= I * 2, which != 2 * I. Addition and multiplication aren't necessarily
commutative for transfinite _ordinal_ [counting] numbers, though they are
for transfinite _cardinal_ [size] numbers.
>I * 2 = ?
= count to I, then start from 1 again and count to I again.
This differs from 2 * I, which means "count to 2 repeatedly, I times" and
gets you to I.
>I * 123 = ?
= I * 123, != 123 * I [ = I].
>I * I = ?
= count to I, then do it again, then repeat, I times.
>I - 10 = ?
= count to I, then count backwards 10 places. It's the "count to I" step that's
"irreversible" in a sense - there's a "jump" there.
>I - 1992 = ?
>I - I = ? Okay the last one can be your oppinion if you like.
It's not really defined. You gotta tell us how you're counting backwards.
>Justification would be nice as well.
Dave "nicely left-justified" DeLaney
Kevin Mendel
AlbertPark wrote:
>
> do...@woozle.dialix.oz.au (Douglas) wrote:
> >What's the problem with this infinity thing?
> >
> >I - I = I.
> >
> >Right?
> Depends. It might sound weird for anyone without some math background
> first I equels the second I then I - I = zero. Of course, just for closer
> sakes, if the second I is bigger then I - I = negative infinity.
Albert's question may be asked in another way.
If you gain infinite life, and then lose infinite life,
is it:
(L + I) - I ... which is 0?
Or is it
L + (I - I) ... which is L?
The answer is, since gains and loses are applied as they occur,
it operates as in the first case, not as in the second case, and
so the answer is you end up with 0.
Your car and gas scenario works as according to the second case,
which is why it gives you a different result.
Kevin