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 …

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 …

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.

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 …

Then, $u$ is surjective iff $\det (u)$ is a unit in $A$, and $u$ is injective iff $\det (u)$ is a regular element of $A$ (i.e. $\det (u)$ is not a zero divisor). Hence a surjective endomorphism of a …

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.