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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 …

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 …

I want to prove that surjectivity is stable under base change: if $f:X\to S$ a surjective morphism of scheme and $\varphi:T\to S$ then $f_T:X\times_S T\to T$ is surjective.

Mar 30, 2020 · If the function is going from A to A, then the cardinality of the domain and codomain are the same, and if it is either surjective or injective, then wouldn't it have to also be …

You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …

Jun 16, 2017 · Whether or not a function like that is surjective becomes an interesting question, not only for solving equations, but for answering other questions about the structure of the …

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 …

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.