I know how to show the cardinality between 2 of the 3 could work. For example, you can establish a bijection with integers and all naturals through $\mathbb{N}$: s(n) = $\sum_{k =1}^n1$ and $\mathbb{Z}$L s(n) = $\sum_{k=1}^n(-1)^{k+1}*k$. I'm having trouble relating the integers to the natural evens.
Original Question: Show (by building the appropriate one-to-one correspondences) that the natural numbers, the even natural numbers, and the integers all have the same cardinality.