Find a one-to-one correspondence from the set of positive integers to the set of all integers (positive, negative, or zero).

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

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