The Size of InfinityDate: 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/ |
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