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)
In*jec"tion\, n. [L. injectio : cf.F. injection.]1. The act of injecting or throwing in; -- applied particularly to the forcible throwing in of a liquid, or a["e]riform body, by means of a syringe, pump, etc. 2. That which is injected; especially, a liquid medicine thrown into a cavity of the body by a syringe or pipe; a clyster; an enema. --Mayne. 3. (Anat.) (a) The act or process of filling vessels, cavities, or tissues with a fluid or other substance. (b) A specimen prepared by injection. 4. (Steam Eng.) (a) The act of throwing cold water into a condenser to produce a vacuum. (b) The cold water thrown into a condenser. Injection cock, or Injection valve (Steam Eng.), the cock or valve through which cold water is admitted into a condenser. Injection condenser. See under Condenser. Injection pipe, the pipe through which cold water is through into the condenser of a steam engine.
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