Fixed Point (mathematics) (it Is A -1 And 0 Branch Function W-Lambert In Point -W(-1) )
Fixed point may refer to: * Fixed point (mathematics), a value that does not change under a given transformation * Fixed-point arithmetic, a manner of doing arithmetic on computers * Fixed point, a benchmark (surveying) used by geodesists * Fixed point join, also called a recursive join The recursive join is an operation used in relational databases, also sometimes called a "fixed-point join". It is a compound operation that involves repeating the join operation, typically accumulating more records each time, until a repetition ma ...

Fixed Point (mathematics)
A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by the function. In physics, the term fixed point can refer to a temperature that can be used as a reproducible reference point, usually defined by a phase change or triple point. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and . For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed point means the point is on the line , or in other words the graph of has a point in common with that line. Fixed-point iteration In numerical analysis, ''fixed-point i ...
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Fixed-point Arithmetic
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation. In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative powers of the base ''b''. The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if ''n'' fraction digits are stored, the value will always be an integer multiple of ''b ...
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Benchmark (surveying)
The term benchmark, bench mark, or survey benchmark originates from the chiseled horizontal marks that surveyors made in stone structures, into which an angle-iron could be placed to form a "bench" for a leveling rod, thus ensuring that a leveling rod could be accurately repositioned in the same place in the future. These marks were usually indicated with a chiseled arrow below the horizontal line. The term is generally applied to any item used to mark a point as an elevation reference. Frequently, bronze or aluminum disks are set in stone or concrete, or on rods driven deeply into the earth to provide a stable elevation point. If an elevation is marked on a map, but there is no physical mark on the ground, it is a spot height. Purpose The height of a benchmark is calculated relative to the heights of nearby benchmarks in a network extending from a ''fundamental benchmark''. A fundamental benchmark is a point with a precisely known relationship to the vertical datum of t ...
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