Assertion: function | /r/HasProperty | injective
Facets:
value: always
type: DEGREE
Source sentences:
text: For example, a function is injective if the converse relation R T ⊆ Y × X {\displaystyle R^{\text{T}}\subseteq
text: The function f is injective (or one-to-one, or is an injection) if f(a) ≠ f(b) for any two different elements a and b of X.
text: An empty function is always injective.
text: As a word of caution, "a one-to-one function" is one that is injective, while a "one-to-one correspondence" refers to a bijective function.
text: The function f is said to be injective provided that for all a and b in X,
text: has only one element, then the function is always injective.
text: Proving that functions are injective [ edit ]
text: A proof that a function f is injective depends on how the function is presented and what properties the function holds.
text: There are multiple other methods of proving that a function is injective.
text: A partial function is said to be injective, surjective, or bijective when the function given by the restriction of the partial function to its domain of definition is injective, surjective, bijective respectively.
text: Furthermore, a function which is injective may be inverted to an injective partial function.
text: A function is bijective if and only if it is both surjective and injective.
text: The functions W k (z), k ∈ Z are all injective and their ranges are disjoint.
text: A function is injective if it is one-to-one.