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## Homework Statement

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.

2. Homework Equations

2. Homework Equations

## The Attempt at a Solution

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

_{1}={k∈ℤ: 2k, k≠0} and A

_{2}={m∈ℤ:2m+1, m≠0}, so that would mean ℙ={A

^{1}, A

_{2}}. 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.