May 14, 2015 · An injective function (a.k.a one-to-one function) is a function for which every element of the range of the function corresponds to exactly one element of the domain.

An example of an injective function $\mathbb {R}\to\mathbb {R}$ that is not surjective is $\operatorname {h} (x)=\operatorname {e}^x$. This "hits" all of the positive reals, but misses zero and all 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 $\rightarrowtail$ or …

A function is bijective if it is both injective and surjective (per definition). So this particular $f$ is bijective since it is both injective and surjective, as explained above.

Oct 12, 2016 · The title should be changed to "Does a function need every element of the domain to map onto some element of the codomain?", since this question applies to all functions, not just …

May 20, 2018 · Is it necessary, that for a function to be injective (one-one) at all points on its domain, it should strictly not be monotonic at any point on its domain? I reckon that this should be true, …

Jan 15, 2013 · Prove that if a continuous function is injective, then it is monotonic Ask Question Asked 13 years, 3 months ago Modified 2 years ago

Since it is strictly increasing and the domain is unbounded hence the function should be unbounded also?

Injective function from $\mathbb {R}^2$ to $\mathbb {R}$? Ask Question Asked 13 years, 7 months ago Modified 6 years, 7 months ago

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.