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#1 2006-06-05 21:03:21

Zmurf
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Registered: 2005-07-31
Posts: 49

Question about Infinity

Something my friend and I were pondering. Wouldn't the difference of infinity and infinity be infinity and not zero?

That is to say, ∞ - ∞ = ∞. I'm basing this on the understanding, however, that infinity is not a constant.


"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."

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#2 2006-06-05 22:16:45

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: Question about Infinity

well i think of it this way

∞ - n = ∞, because no matter what n is, ∞ - n is still going to be infinately big
but ∞ - ∞, i think of it as being, ∞ is infinately big, no matter what number you take away from it, its never going to be big enough unless its ∞...


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#3 2006-06-05 23:20:35

MathsIsFun
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Registered: 2005-01-21
Posts: 7,555

Re: Question about Infinity

How about this: start travelling in a circle until you reach the end.

What's that you say? There is no end? Ah ... good.

Now, if you add or subtract some known distance from your circular travels, you still won't reach an end.

However, if you throw in another infinity ... (excuse me while my brain explodes)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-06-06 00:52:29

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Question about Infinity

The only reasonable (mathimatical) way to talk about infinity in this context is to do so with limits.

∞ - ∞ is known as an indeterminate form.

Here, we certainly have ∞ - ∞, but it's "equal" to zero.  That is to say, that both the infinities are the same size.

Here, we again have ∞ - ∞, but this time it "equals" ∞.  That is because the 2n infinity is larger than the n infinity.

And finally, -∞.

Now it can also be any other value.

Let f(n) = (n + r) - n, where r is a real number.

Then:

Which is in the form of ∞ - ∞, but the result will be a real number, r.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2006-06-06 18:48:13

George,Y
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Registered: 2006-03-12
Posts: 1,306

Re: Question about Infinity

Ricky, you see. That's why I tend to be conservative about infinity and would rather treated as a variable but not a reached thing. To think it as stable is natural, but that brings along too many bugs.


X'(y-Xβ)=0

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#6 2006-06-06 19:39:25

Zmurf
Member
Registered: 2005-07-31
Posts: 49

Re: Question about Infinity

But you can't have 2∞ can you? 2∞ would just be infinity. If ∞ - ∞ = 0, then 2∞ - ∞ = 0 too as well as ∞² - √∞ = 0.

But I was also thinking about the universe. It was described to have begun as a single point infinitesimal (is that the word?). If this is so than it would be impossible for the universe to be of any real size at this stage unless its size was increased by infinity would make the size be ... bah now my brain hurts.


"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."

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#7 2006-06-06 22:04:21

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Question about Infinity

Personal theory:

Thermodynamics tells us that the Universe is becoming more "disordered", and disorder is more "likely" (for example toss 10 coins and the likelihood of them all being heads or tails is very small, the likelihood of 5 heads is relatively high).

Thus the Universe was more orderly and in a less likely state, and if you project that back to the limit, then the Universe started as totally orderly and unlikely.

Discuss smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#8 2006-06-07 02:38:41

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Question about Infinity

a single point infinitesimal of universe..
I don't know if this holds or not, but I do know around two thousands years ago, there was a great philosopher as well as a excellent logician who challenged space is made of infinite infinitesimals. His name was Zeno.

I wish String Theory may some day prove time and space together is made of sufficient simals instead of infinitesimals. And I wish I be alive that day. big_smile


X'(y-Xβ)=0

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#9 2006-06-07 10:34:16

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Question about Infinity

Perhaps a better way to think about the universe is as a set of relationships. (Example: think of the line rather than the two end-points.) In that case there are no "things", just relationships.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2006-06-08 03:56:34

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: Question about Infinity

Acording to the almighty wikipedia.org (:])


is an undefined operation...

linky linky

Last edited by Patrick (2006-06-08 03:58:14)


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#11 2006-06-08 23:53:44

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Question about Infinity

The problem is that ∞ - ∞ can be anything. Consider the following examples, which are limits in the form ∞ - ∞:



Another example with a different result is as follows:







These two examples serve to support the following statements: ∞ - ∞ is not necessarily ∞ or 0. Since infinity is more of a concept and not an exact value, there are infinitely many infinities. Several different infinities were seen in the above examples. Because of this quality of ∞, ∞ - ∞ has infinitely many solutions.

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#12 2006-06-10 06:26:54

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Question about Infinity

It can be anything!!!
It is well-defined "undefinity".
(We can assume that there exists an "object" undef, such that by definition: n/0=UD; inf-inf=UD ect.)
We have 0,inf,und (undefined) Here's a system of definition rules:

inf - inf := und;
inf / inf = 0 / 0 := und;
inf / 0 = 0 / inf := und;
inf * 0 := und;
und +-*/ all others :=und;

Last edited by krassi_holmz (2006-06-10 06:28:12)


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#13 2006-07-21 01:08:11

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: Question about Infinity

if ∞-n=∞ and ∞-∞=0, that means that ∞-∞-n=0, and that means that ∞-∞=n=anything

Last edited by Kurre (2006-07-21 01:09:03)

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