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Find a one-to-one correspondence from the set \mathbb{N} of positive integers to the set \mathbb{Z} of all integers (positive, negative, or zero).  \\ \[ \mathbb{N} \in 1,2,3,4,5,6,7 \]  \[ \downarrow \thinmuskip \>  \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \] \[ \mathbb{Z} \in {-3, -2, -1, 0, 1, 2, 3} \]