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In one direction, if = + is a complex number whose real part and imaginary part are both constructible real numbers, then replacing and by their formulas within the larger formula + produces a formula for as a complex number. In the other direction, any formula for an algebraically constructible complex number can be transformed into formulas ...
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language.
A computable number [is] one for which there is a Turing machine which, given n on its initial tape, terminates with the nth digit of that number [encoded on its tape]. The key notions in the definition are (1) that some n is specified at the start, (2) for any n the computation only takes a finite number of steps, after which the machine ...
Constructible function, a function whose values can be computed in a number of steps or a number of Turing-machine cells of order given by the function itself Topics referred to by the same term This disambiguation page lists articles associated with the title Constructibility .
Tuple in Standard ML, Python, Scala, Swift, Elixir; List in Common Lisp, Python, Scheme, Haskell; Fixed-point number with a variety of precisions and a programmer-selected scale. Complex number in C99, Fortran, Common Lisp, Python, D, Go. This is two floating-point numbers, a real part and an imaginary part. Rational number in Common Lisp
Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b −1 for every nonzero element b.
The function f such that f(n) = 1 if there is a sequence of at least n consecutive fives in the decimal expansion of π, and f(n) = 0 otherwise, is computable. (The function f is either the constant 1 function, which is computable, or else there is a k such that f(n) = 1 if n < k and f(n) = 0 if n ≥ k. Every such function is computable.