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 · is surjective and seems to contain the same information as f f. But wait, is it really the same? Of course both functions f f and f~ f have exactly the same output when applied to an element …

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Understanding the definition of surjective function Ask Question Asked 8 years, 3 months ago Modified 8 years, 3 months ago

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.

Apr 10, 2011 · 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, …

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 cube it we get …

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 $\\rightarrowtail$ or $\\

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 always surjec...

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 …