Noun
surjection (plural surjections)
(set theory) A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function
f
:
X
→
Y
{\displaystyle f:X\rightarrow Y}
for which for every
y
∈
Y
{\displaystyle y\in Y}
, there is at least one
x
∈
X
{\displaystyle x\in X}
such that
f
(
x
)
=
y
{\displaystyle f(x)=y}
.
Every function with a right inverse is necessarily a surjection. Source: Internet
If there is a surjection from A to B that is not injective, then no surjection from A to B is injective. Source: Internet
More precisely, every surjection f : A → B can be factored as a projection followed by a bijection as follows. Source: Internet
With this terminology, a bijection is a function which is both a surjection and an injection, or using other words, a bijection is a function which is both "one-to-one" and "onto". Source: Internet