The notation f:S→T denotes that f is a function, also called a map , defined on all of a set S and whose outputs lie in a set T
. A function f:S→T is injective if for all x,y∈S , f(x)=f(y) implies that x=y . Alternatively: a function is injective if we can uniquely recover some input x based on an output f(x) . What functions are injective?