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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 …

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.

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 …

For one, you can talk about a function being surjective if the domain and codomain are simply sets, but you cannot talk about a function being continuous unless the domain and codomain …

Oct 24, 2020 · For Banach spaces $X$ and $Y$, a bounded operator $A: X\to Y$ is also bounded below iff the adjoint $A^*: Y^*\to X^*$, defined as $A^*: f\mapsto f\circ A$, is surjective.

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 …

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

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 …