To prove a function is bijective, you need to prove that it is injective and also surjective. "Injective" means no two elements in the domain of the function gets mapped to the same image.

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 $\\

Nov 22, 2021 · What's the difference between Injective and Bijective? For example, is there a more rigorous proof of the bijectivity of a function? Also, can these properties be applied to more than just …

Sep 3, 2017 · I know that in order for a function to be invertible, it must be bijective, but does that mean that all bijective functions are invertible?

The point being that the bijective property should actually refer to the "one-to-one" nature of the relation or function in question. (Functions get uniquely defined 'for free'. The extra ingredient for a bijective …

May 16, 2015 · Bijective means both injective and surjective. This means that there is an inverse, in the widest sense of the word (there is a function that "takes you back"). The inverse is so-called two …

Apr 15, 2020 · An isomorphism is a bijective homomorphism. I.e. there is a one to one correspondence between the elements of the two sets but there is more than that because of the homomorphism …

Jan 11, 2016 · I am very familiar with the concepts of bijective, surjective and injective maps but I am interested in improvising the definition of bijection in a way I have not seen done before. To be clear I …

Jun 19, 2017 · I am trying to prove a topology statement. Let $X,Y$ be topological spaces, and let $f: X \\to Y$ be a bijection. Prove that $f$ is a homeomorphism if and only if $f ...

The proof is correct. It might be easier to prove that the composition of bijective functions is still bijective and use the fact that $y=x^3$ is bijective.