Math Is Fun Forum

regnar998

Member

Registered: 2009-05-08

Posts: 10

Infinity minus infinity

I've come across this weird little puzzle,

Infinity - Infinity = ???

Now when you first look at this you might think it equals zero. But look at it like this:

If you have infinity marbles and you give infinity (As in all of them) to someone else then infinity - infinity = nothing.
But if you have infinity marble numbered 1, 2, 3 etc. and gave every second marble to someone then infinity - infinity = infinity
BUT if you give someone else all the marbles numbered 3 or above (Which is infinity marbles) then infinity - infinity = 2.
But the question is in all these examples are you really giving infinity marbles away and do you still have infinity (Or whatever) left???

What do you guys think anyway?:)

Regnar

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The 186,557,266-186,557,274 digits of PI is 12345678.             (tinyurl.com/pisearch)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Infinity minus infinity

Hi regnar998;

Welcome to the forum. Look at this.

There is no single answer to this, as infinity is not a number in the strictest sense. 
Infinity is a "limit".  It is something you can get closer and closer to, but you never
quite reach it.  What matters is how fast you approach the first infinity (call it
infinity01) versus how fast you approach the second infinity (call it infinity02).  If
you approach both at exactly the same speed, always the same distance from each, then
infinity01-infinity02=0.  If you are always a little closer to infinity01, then
infinity01-infinity02 is a positive number.  If you move toward infinity01 twice as
fast as how you approach infinity02, then infinity01-infinity02=infinity.  The behavior
of limits is not quite the same as the behavior of numbers.

Dr. Ken Mellendorf

I agree with some of this and some I am not sure of. Lets wait for some of the other posters who are way more rigorous to settle the question.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathaholic

Member

From: Earth

Registered: 2012-11-29

Posts: 3,251

Re: Infinity minus infinity

Indeterminate!

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Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

Calligar

Member

Registered: 2011-09-24

Posts: 272

Re: Infinity minus infinity

I would say undefined because infinity isn't a number.  Infinity can be a difficult concept to understand when using it in ways such as that.  I might suggest you look here to find out more about it...

http://www.mathsisfun.com/numbers/infinity.html

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There are always other variables.  -[unknown]
But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end.  -Aristotle
Everything makes sense, one only needs to figure out how.  -[unknown]

mathaholic

Member

From: Earth

Registered: 2012-11-29

Posts: 3,251

Re: Infinity minus infinity

He said undefined.

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Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

mathaholic

Member

From: Earth

Registered: 2012-11-29

Posts: 3,251

Re: Infinity minus infinity

I said indeterminate.

Indeterminate means you cannot tell the answer, because of infinity, meaning forever.

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Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate