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 …

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 …

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 …

Oct 29, 2020 · Wikipedia uses this picture for injective and surjective functions. The top right is non-surjective. I have added a mapping on, is this now surjective? Why/why not?

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 …

Jan 5, 2016 · @Antoras: It does not mean that every injective function is not surjective. It just means that some injective functions are not surjective, and some surjective functions are not …

Mar 30, 2020 · A function that is not surjective means that f: Z → Z f: Z → Z means f f maps to some of Z Z but not all. Can you think of any examples? What about a function that maps to …