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