injection

in·jec·tion   (ĭn-jěk'shən)    n.   The act of injecting. Something that is injected, especially a dose of liquid medicine injected into the body. Mathematics A function that is one-to-one. [Sense 3, in-2 + (pro)jection.]

Main Entry: in·jec·tion
Pronunciation: in-'jek-sh&n
Function: noun
1 a : the act or an instance of injecting a drug or othersubstance into the body b : a solution (as of a drug) intended for injection (as by catheter or hypodermic syringe) either under or through the skin or into the tissues, a vein, or abody cavity c : an act or process of injecting vessels or tissues; also : a specimen prepared by injection
2 : the state of being injected : CONGESTION —see CIRCUMCORNEALINJECTION

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

1. The act of injecting a substance into a tissue, vessel, canal, or organ.

2. Something that is injected, especially a dose of liquid medicine injected into the body.

3. Congestion or hyperemia.

injection
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)