Injection

[in-jek-shuh n] /ɪnˈdʒɛk ʃən/

noun
1.
the act of .
2.
something that is .
3.
a liquid into the body, especially for medicinal purposes, as a hypodermic or an enema.
4.
state of being hyperemic or bloodshot.
5.
Mathematics. a one-to-one function.
6.
Also called insertion. Aerospace. the process of putting a spacecraft into orbit or some other desired trajectory.
/ɪnˈdʒɛkʃən/
noun
1.
fluid injected into the body, esp for medicinal purposes
2.
something injected
3.
the act of injecting
4.

5.
(maths) a function or mapping for which f(x) = f(y) only if x = y See also surjection, bijection
n.

“forcing a fluid into a body” (with a syringe, etc.), early 15c., from Middle French iniection (14c.) or directly from Latin iniectionem (nominative iniectio), noun of action from past participle stem of inicere (see inject).

injection in·jec·tion (ĭn-jěk’shən)
n.

injection
(ĭn-jěk’shən)

1. A function, f : A -> B, is injective or one-one, or is an injection, if and only if
for all a,b in A, f(a) = f(b) => a = b.
I.e. no two different inputs give the same output (contrast many-to-one). This is sometimes called an embedding. Only injective functions have left inverses f’ where f'(f(x)) = x, since if f were not an injection, there would be elements of B for which the value of f’ was not unique. If an injective function is also a surjection then is it a bijection.
2. An injection function is one which takes objects of type T and returns objects of type C(T) where C is some type constructor. An example is
f x = (x, 0).
The opposite of an injection function is a projection function which extracts a component of a constructed object, e.g.
fst (x,y) = x.
We say that f injects its argument into the data type and fst projects it out.
(1995-03-14)