3 ms·
> injections on finite sets are also surjections Not necessarily [1]. I think you're missing an assumption there. [1] https://en.wikipedia.org/wiki/Injective
by csense 1y ago
> injections on finite sets are also surjections
Not necessarily [1]. I think you're missing an assumption there.
[1] https://en.wikipedia.org/wiki/Injective_function#/media/File:Injection.svg https://en.wikipedia.org/wiki/Injective_function#/media/File...
- MaxRegret 1y agoIn this case, multiplication by any nonzero fixed element of the ring is an injection from the ring to itself. Any injection from a finite set to itself is indeed a surjection (and so also a bijection).
- susam 1y agoThe intended point, I believe, is the fact that any injective function from a finite set to itself is also surjective.