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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hy everyone!

What do you think about operations with infinity?

We know that ∞ : ∞ = indeterminate, but what about ∞ * ∞ ?

The result is ∞ ?

A friend of mine suggest this:

n^3 : n = n^2

so

∞^3 : ∞ = ∞^2

so

∞ : ∞ = ∞^2

which means

∞^2 = indeterminate.

Any feedback is welcome.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi;

So you suggest that infinity multiplied by infinity equals infinity?

By the way, there are just two hypothesis about this operation.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Hi;

Yes, I think that ∞ * ∞ = ∞.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

Mpmath wrote:

Hi;

So you suggest that infinity multiplied by infinity equals infinity?

By the way, there are just two hypothesis about this operation.

Of course. One is that infinity*infinity=infinity and the second is that multiplication is not an operation that should be applied to infinity.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

And way about n : infinity?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Hi;

How do you map n to infinity?

Oh wait, I am sorry this : is a division operator. My browser is reading it wrong. Division is not allowed.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Sorry, bobbym, n to infinity or n : infinity?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Hi;

I did not understand your notation. First let's get that right. What are you saying here:

n^3 : n = n^2

I am not following that.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi;

The most Plausible hypothesis is 0, But if n : infinity = 0 means that n : 0 = infinity, which is impossible. I think that 0 is the batter hypothesis, But I would not exclude infinity. Answers are many.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Regarding the second post n^3: n = n^2 is a simple formula, applied to infinity shows that infinity*infinity = indeterminate.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Hi;

n^3: n = n^2 is a simple formula

You are saying n^3 to n is n^2? What does "to" mean here? I am not following that.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,071

hi Mpmath

Can I suggest you type 'divided by' to remove the confusion?

Bob

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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Sorry, this means n^3 divided n= n^2.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

By the way, I Will use dividev by from now, thanks!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Yes, that is what I thought. Okay, you can divide n^3 by n as long as n does not equal 0 or ∞.

is indeterminate.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Yes, that's what I was thinking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

But

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Ok. This is most Plausible hypothesis.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Hi;

Yes, infinity is not a number. Some programming languages say NAN for it. Therefore, you can not add or subtract or perform any other type of arithmetic on it and expects consistent results with the number system. There is a small movement in mathematics, but growing, to eliminate it entirely.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi;

This small movement wants to eliminate infinity or operations with infinity?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

Eliminate infinity entirely.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

I think that eliminate infinity is absurd. Infinity is a way to define where numbers and universe can arrive.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,671

They believe like others that the concept of infinity is full of holes. It really does not belong in mathematics and could be replaced. I am not expert on this part of math and therefore do not know enough to decide who is right.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Well, no one can decide what is better Regarding infinity, we can only have a theory.

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