Home Articles FAQs XREF Games Software Instant Books BBS About FOLDOC RFCs Feedback Sitemap


You are here: irt.org | FOLDOC | injection

1. <mathematics> 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. <reduction> 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.


Nearby terms: Initial Program Load « Initial Program Loader « initiator « injection » inkjet printer » ink printer » inline

FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL

©2018 Martin Webb