Fixed point

In mathematics, a fixed point of a function is a point that is mapped to itself by the function. For example, if f is defined on the real numbers by f(x) = x² − 3x + 4, then 2 is a fixed point of f, because f(2) = 2.

See also

• Brouwer fixed point theorem
• Banach fixed point theorem
• Knaster-Tarski theorem
• Y combinator / fixed point combinator
• Fixed point theorems about recursive functions

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In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the decimal (or binary or hexadecimal) point. For example, a fixed-point number with 4 digits after the decimal point could be used to store numbers such as 1.3467, 281243.3234 and 0.1000, but would round 1.0301789 to 1.0302 and 0.0000654 to 0.0001. These fixed-point presentations are usually used, if either the executing processor does not have any floating point unit (FPU) or performance outrules exactness.