Sentences with INJECTIVE
Check out our example sentences below to help you understand the context.Sentences
1
"An injective function has the property that different elements in the domain map to different elements in the codomain."
2
"The function f(x) = 2x is an injective function because different inputs always produce different outputs."
3
"In linear algebra, a linear transformation is called injective if the only vector mapped to the zero vector is the zero vector itself."
4
"An injective mapping preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain."
5
"The injective function f(x) = x^3 is a one-to-one correspondence between real numbers and their cubes."
6
"An injective function can be thought of as a 'one-to-one' function since it maps distinct elements to distinct images."
7
"In set theory, an injective function between two sets A and B is formally defined as a function 'f' such that for every two elements 'a1' and 'a2' in A, if f(a1) = f(a2), then a1 = a2."
8
"An injective linear map between two vector spaces is sometimes called a monomorphism."
9
"An injective function preserves equality: if two elements in the domain are equal, their images in the codomain are also equal."
10
"An example of an injective function is f(x) = x + 5, where different inputs always yield unique outputs."
1
"An injective function sends distinct elements in the domain to distinct elements in the codomain."
2
"A linear map between vector spaces is injective if and only if its null space is trivial."
3
"The injective function f(x) = x² maps distinct real numbers to distinct positive numbers."
4
"An injective mapping is also called a one-to-one mapping."
5
"The function f(x) = e^x is injective on the set of real numbers."
6
"An injective homomorphism preserves the operation and the identity of the algebraic structure."
7
"A composition of two injective functions is injective."
8
"An injective function cannot map two different elements in the domain to the same element in the codomain."
9
"If a function is injective, then for every y in the codomain, there is at most one x in the domain such that f(x) = y."
10
"The inclusion mapping of a subset into a set is injective."
11
"An injective function does not lose any information in the process of mapping."
12
"A function f: X → Y is injective if and only if it has a left inverse."
13
"An injective function cannot have two distinct elements in the domain that map to the same element in the codomain."
14
"An injective matrix must have linearly independent columns."
15
"An injective function is also called a one-to-one function."
16
"The function f(x) = x³ is injective on the set of real numbers."
17
"An injective function can have multiple left inverses."
18
"An injective function has a unique inverse function over its range."
19
"The cardinality of the range of an injective function is equal to the cardinality of its domain."
20
"An injective function preserves distinctness of elements in the domain."
