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Calculus and Beyond Homework Help
Examples of Partitions: How to Divide Nonzero Integers into Infinite Sets?
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[QUOTE="ver_mathstats, post: 6149912, member: 650531"] [h2]Homework Statement [/h2] Show an example of a partition of the nonzero integers into two infinite sets. Show an example of a partition of the nonzero integers into infinitely many sets, such that each set of the partition contains exactly two elements. [B] 2. Homework Equations [/B][h2]The Attempt at a Solution[/h2] I know that a partition A is a collection of subsets {Ai}. An example of a partition of the nonzero integers into two infinite sets would be A[SUB]1[/SUB]={k∈ℤ: 2k, k≠0} and A[SUB]2[/SUB]={m∈ℤ:2m+1, m≠0}, so that would mean ℙ={A[SUP]1[/SUP], A[SUB]2[/SUB]}. Am I on the write track with this? I assume since ever number is either odd or even then I could write two sets with even and odd numbers that are infinite but do not include 0. I am confused how to give an example for the second part however? Thank you. [/QUOTE]
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Examples of Partitions: How to Divide Nonzero Integers into Infinite Sets?
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