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When a function is said to be as one to one function

A function f is said to be one-to-one (injective) , if and only if whenever f(x) = f(y) , x = y .

Example: The function f(x) = x2 from the set of natural numbers N to N is a one-to-one function.

Note that f(x) = x2 is not one-to-one if it is from the set of integers (negative as well as nonnegative) to N, because for example f(1) = f(-1) = 1 .