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Even and Odd numbers
Posted by: Anonymous User (89.243.166.---)
Date: July 19, 2008 11:13PM
I know it's not possible to have more Odd than Even numbers, as both are infinite.
But how on earth does someone discover a thing like this?
Edited 1 time(s). Last edit at 07/19/2008 11:16PM by Billfred.
But how on earth does someone discover a thing like this?
Edited 1 time(s). Last edit at 07/19/2008 11:16PM by Billfred.
Re: Even and Odd numbers
Posted by: MuseSusan (---.union.edu)
Date: July 20, 2008 01:36AM
<mathematician mode>
Saying that both the set of even numbers and the set of odd numbers are infinite is not enough, actually. The set of integers and the set of real numbers are both infinite, but the set of reals is bigger than the integers in a very rigorous way. On the other hand, the sets of evens, odds, integers, and rational numbers are all the same size (even though there are infinitely many rational numbers between each pair of integers!) because we can put each set in one-to-one correspondence with each of the others.
</mathematician mode>
If you want more explanation, go right ahead (there are a few of us who would be delighted to expound on the joys of infinite sets), but I'll stop here for fear of making heads explode.
Welcome to the fforum!
Saying that both the set of even numbers and the set of odd numbers are infinite is not enough, actually. The set of integers and the set of real numbers are both infinite, but the set of reals is bigger than the integers in a very rigorous way. On the other hand, the sets of evens, odds, integers, and rational numbers are all the same size (even though there are infinitely many rational numbers between each pair of integers!) because we can put each set in one-to-one correspondence with each of the others.
</mathematician mode>
If you want more explanation, go right ahead (there are a few of us who would be delighted to expound on the joys of infinite sets), but I'll stop here for fear of making heads explode.
Welcome to the fforum!
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