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I am a 9th grader self-studying about set theory and functions. I understood most basic concepts, but I didn't understand what is a surjective function. I have understood what is an injective funct...

Update: In the category of sets, an epimorphism is a surjective map and a monomorphism is an injective map. As is mentioned in the morphisms question, the usual notation is …

Then, $u$ is surjective iff $\det (u)$ is a unit in $A$, and $u$ is injective iff $\det (u)$ is a regular element of $A$ (i.e. $\det (u)$ is not a zero divisor). Hence a surjective endomorphism of a …

Apr 11, 2023 · Is the function surjective, injective or bijective?". My (simplified) understanding of a injective function is that every value for X has to map to a unique value on Y.

What you're trying to prove is that surjectivity is stable under base change, not that it is local on the target.

Here you don't care about domains and codomains. This is often good enough for practical considerations. But from the formal viewpoint, it doesn't make sense to ask whether this …

Nov 1, 2015 · Is an isometry necessarily surjective? Ask Question Asked 10 years, 1 month ago Modified 10 years ago

I have the same feeling as yours: often, proving that a linear map is injective is easier than proving it is surjective. Of course we are talking about infinite-dimensional vector spaces, otherwise …

Aug 14, 2019 · I use the fact that a composition of injections is injective and a composition of surjections is surjective. I also use the definition of finite where injective $\iff$ surjective within …