An identity functionf is a function which doesn't have any effect: it always returns the same value that was used as its argument.
Formally, if M is a set, we define the identity function idM on M to be that function with domain and codomain M which satisfies
idM(x) = x for all elements x in M.
If f : M → N is any function, then we have f o idM = f = idN o f. In particular, idM is the identity element of the monoid of all functions from M to M.
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
A function is surjective (onto) if every element of the codomain is mapped to by some element (argument) of the domain; some images may be mapped to by more than one argument.
A bijective function is a bijection (one-to-one correspondence).
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