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\section{Finding One to One Correspondence}  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).  \\ \[ \mathbb{N} \in \>1  \> ,2,3,4,5,6,7 1, \> \> \> \> 2, \> \> 3, \> \> 4, \> \> 5, \> \> 6, \> \> 7  \] \[ \downarrow \> \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \]  \[ \mathbb{Z} \in {-3, -2, -1, 0, 1, 2, 3} \]