The Size of Infinity

Date: 09/03/98 at 17:32:38
From: Michael brook
Subject: Infinity qestions

What is infinity x 2? Please help.

Date: 09/03/98 at 19:19:41
From: Doctor Stacey
Subject: Re: Infinity qestions

Hi Michael,

Thanks for submitting your question to Dr. Math. That's a very good 
question, about a very confusing topic. Because infinity isn't 
something we can see or experience, it baffles us easily.

The answer to your question is that there is no answer. Infinity is a 
concept, not a number, so we can't do arithmetic with it. We use the 
word or symbol for infinity because we have no other way to describe 
the concept of infinity, since it is beyond our perceptions.  

Let me give you an example of why your question has no answer.  
Consider the set of all positive even numbers, or 2, 4, 6, 8, ....  
There is an infinite amount of these (call them elements of the set), 
since we can keep on counting them forever. Now think of the regular 
counting numbers, or natural numbers: 1, 2, 3, 4, .... It would seem 
that there are twice as many numbers in this set, so it would be twice 
as big as infinity. However, we can prove that there are the same 
number of elements in each set. Take each of the counting numbers and 
double them. You get the positive even integers. So for every element 
in the set of natural numbers, double it to get its corresponding 
element in the set of positive even integers. This is what is called a 
one-to-one correspondence, and if you can draw a one-to-one 
correspondence between the elements of two sets, then they have the 
same size.

Now that's a lot of information, and confusing information at that.  
If you have more questions, or you don't understand, feel free to 
write back. Good luck!

- Doctor Stacey, The Math Forum
Check out our web site! http://mathforum.org/dr.math/