Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**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.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**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.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

Hi;

Yes, I think that ∞ * ∞ = ∞.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

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

And way about n : infinity?

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

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

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

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

Offline

**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.

Winter is coming.

Offline

**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.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

hi Mpmath

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

Bob

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

Offline

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

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

Winter is coming.

Offline

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

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

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

Offline

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

Yes, that's what I was thinking.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

But

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

Offline

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

Ok. This is most Plausible hypothesis.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

Offline

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

Hi;

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

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

Eliminate infinity entirely.

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

Offline

**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.

Winter is coming.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,562

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.**

Offline

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

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

Winter is coming.

Offline