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December 15th, 2015, 06:52 AM   #1
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Demonstrate set equivalence

Demonstrate 1-to-1 correspondence between the set of whole numbers and integers.

My attempt...

I first divided the set of whole numbers into the two sets of odd numbers and even numbers.

Then I showed 1-to-1 correspondence between
1. The whole numbers (0 and the positive integers) and even numbers
0 to 0, 1 to 2, 3 to 6, n to 2n...
2. The set of negative integers and odd numbers
1 to -3, 3 to -2, 5 to -3, n to (n + 1)/(-2)...

I then conclude that since the set of even and odd numbers is the set of whole numbers, I have, in the manner above, shown a 1-to-1 correspondence between the whole numbers and integers.

Is this acceptable? Is there a better way to do this? Thanks.
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December 15th, 2015, 06:27 PM   #2
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It is essentially correct (some minor errors). It is more cumbersome than necessary.

Simple way to order whole numbers 0,-1,1,-2,2,-3,3,.......
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