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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
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 A1={k∈ℤ: 2k, k≠0} and A2={m∈ℤ:2m+1, m≠0}, so that would mean ℙ={A1, A2}. 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.