Injectivity is a property of functions, not relations.

The domain of a relation is the set of all first elements in the ordered pairs.

A function is a relation that assigns to each element of a set a unique element of another set.

The range of a function is the set of all second elements in the ordered pairs.

A function is injective if it preserves distinct elements, meaning different inputs always produce different outputs.

A function is surjective if every element in the codomain is the output of at least one element in the domain.

A function is bijective if it is both injective and surjective.

The inverse of a function is the function that undoes the original function.

An equivalence relation is a relation that is reflexive, symmetric, and transitive.

The composition of two functions (f) and (g) is (h(x) = f(g(x))).

A many-to-one function is a function where multiple inputs can map to the same output.

A one-to-many function is a function where one input can map to multiple outputs.

The domain of a function is the set of all possible input values.

A function is continuous at a point if the limit of the function as the input approaches that point exists and is equal to the value of the function at that point.