A surjective function is a function that "hits everything": so, for example, the function f(x) = 2x is surjective as a function from R to R, since - for any real a - a 2 is also a real number, and we have f(a …

Understanding the definition of surjective function Ask Question Asked 8 years, 2 months ago Modified 8 years, 2 months ago

On topic: Surjective means that every element in the codomain is "hit" by the function, i.e. given a function f: X → Y f: X → Y the image im(X) i m (X) of f equals the codomain set Y Y. To prove that a …

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 …

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. I …

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 …

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 …

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...

Nov 16, 2020 · An injective function is specifically a function where every element in the codomain appears at most once as the second entry in an ordered pair in the relation. A bijective function is …

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 …