High Quality Content by WIKIPEDIA articles! In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is a point that is mapped to itself by the function. That is to say, x is a fixed point of the function f if and only if f(x) = x. Not all functions have fixed points: for example, if f is a function defined on the real numbers as f(x) = x + 1, then it has no fixed points, since x is never equal to x + 1 for any real number. In graphical terms, a fixed point means thepoint (x, f(x)) is on the line y = x, or in other words the graph of f has a point in common with that line. The example f(x) = x + 1 is a case where the graph and the line are a pair of parallel lines.

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