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...

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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 …

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.

Sep 11, 2024 · Surjective functions need not possess simply defined inverses, but if you can write down an inverse function that is defined on the entire codomain, then of course the function is …

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 …

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 …

Jan 4, 2021 · Can you explain if the inverse of a bijective function is always a bijection, and the same for the inverses of a surjection and injection (i.e. is the inverse of a surjective function …

Nov 22, 2017 · To show a function is surjective, for any element in the codomain we have to show their is an element in the domain that maps to it. Is there an natural number that when we …