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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...

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 function.

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 surjective.

Intuitive definition of injective, surjective and bijective Ask Question Asked 8 years, 5 months ago Modified 5 years, 10 months ago

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 are topological …

Understanding the definition of surjective function Ask Question Asked 8 years, 5 months ago Modified 8 years, 5 months ago

Yes, surjective is kind of weird like that. But in questions that come up, usually there are two spaces we start with then we want to see if a function from one to the other is surjective, and it may not be easy.

Nov 11, 2015 · Added: A correct count of surjective functions is tantamount to computing Stirling numbers of the second kind. The Wikipedia section under Twelvefold way has details.

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 the two are …