Can a function map into or out of the null set?

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SUMMARY

A function can map out of a null set, but it does not perform any action, similar to the identity function. It can also map into a null set, provided that the domain contains exactly zero elements; otherwise, it would require mapping to a value. Both scenarios result in the empty function, as highlighted by user jbunniii in the discussion.

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Can a function involve a mapping into or out of a null set?
 
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Gear300 said:
Can a function involve a mapping into or out of a null set?

Out of: yes, but it doesn't do anything (in an even more literal sense than the identity function doesn't do anything).

Into: Yes, but if it's a function rather than a partial function the domain must have exactly zero elements (because if it had even one it would have needed to map that to something).

So in both cases it's just the empty function, as jbunniii points out.
 

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