Wiktionary
a. (context computing English) Pertaining to fixed point#Noun representations or operations. alt. (context computing English) Pertaining to fixed point#Noun representations or operations. n. 1 (context computing English) A fractional-number representation with a fixed number of digits after the decimal point. Compare floating point and integer. 2 (context mathematics English) A value which is unchanged by a function or other mapping. Formally: a value ''x'' for which ''f''(''x'') = ''x''.Fixed point (mathematics)
Wikipedia
"Fixed point" has many meanings in science, most of them mathematical.
- Fixed point (mathematics)
- Fixed-point iteration, a general method to compute the fixed point of an iterated function.
- Fixed-point combinator
- For "Fixed-point join" in databases, see Recursive join
- Fixed-point arithmetic, a manner of doing arithmetic on computers
- Benchmark (surveying), fixed points used by geodesists
- For “fixed points” in physics, see Renormalization group
- Fixed points are necessary for a watercraft to be moored to a quay.
- Archimedes said δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω, which is sometimes translated as “Give me a fixed point and I will move the world.”
- Fixed point, in the "Doctor Who" episode The Wedding of River Song, a point in time that can not be changed
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function. That is to say, c is a fixed point of the function f(x) if and only if f(c) = c. This means f(f(...f(c)...)) = f(c) = c, an important terminating consideration when recursively computing f. A set of fixed points is sometimes called a fixed set.
For example, if f is defined on the real numbers by
f(x) = x − 3x + 4,
then 2 is a fixed point of f, because f(2) = 2.
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 the point (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.
Points that come back to the same value after a finite number of iterations of the function are called periodic points. A fixed point is a periodic point with period equal to one. In projective geometry, a fixed point of a projectivity has been called a double point.
In Galois theory, the set of the fixed points of a set of field automorphisms is a field called the fixed field of the set of automorphisms.
Usage examples of "fixed point".
Lastly, with a quick and easy motion, it, cast the lance toward the sky, whence it fell, remaining fixed point downward in the earth.
Another stir of movement in the middle distance caught her eye: a free cloak, seemingly riding an updraft over a fixed point.
The one fixed point in his immediate future was that his leave was over and that he must be back at his post in London the next morning.
Carefully, with the wind as my one fixed point, I searched the ground, patterning it in squares.
He just looked around him once, in a sweeping, all-embracing stare, that didn't come to a head on any one fixed point, didn't centre at all.
Germaine was a whore all the way through, even down to her good heart, her whore's heart which is not really a good heart but a lazy one, an indifferent, flaccid heart that can be touched for a moment, a heart without reference to any fixed point within, a big flaccid whore's heart that can detach itself for a moment from its true center.
Even then, at that fixed point in time, I was not certain of what I intended to do.