notion of definable numbers has at most countably many definable real numbers. However, by Cantor's diagonal argument, there are uncountably many real numbers...

Look up definable in Wiktionary, the free dictionary. In mathematical logic, the word definable may refer to: A definable real number A definable set A...

axioms of ZF, a well ordering of the real numbers can be shown to be explicitly definable by a formula. A real number may be either computable or uncomputable;...

shows that there is a definable, countably saturated (meaning ω-saturated but not countable) elementary extension of the reals, which therefore has a...

a type of real number that is Turing equivalent to the halting problem. Both of these examples in fact define an infinite set of definable, uncomputable...

compass construction problem put forth by Pappus. Computable number Definable real number Kazarinoff (2003), pp. 10, 15; Martin (1998), p. 41, Corollary...

language Principia Mathematica Hilbert's program Impredicative Definable real number Algebraic logic Boolean algebra (logic) Dialectica space categorical...

therefore it is definable in under sixty letters, and is not the smallest positive integer not definable in under sixty letters, and is not defined by this expression...

π: Every point of the number line corresponds to a unique real number, and every real number to a unique point. Using a number line, numerical concepts...

parameters in the defining formula). A function is definable in M {\displaystyle {\mathcal {M}}} (with parameters) if its graph is definable (with those parameters)...

In mathematics, the extended real number system is obtained from the real number system R {\displaystyle \mathbb {R} } by adding two elements denoted...

imaginary number is the product of a real number and the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is...

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary...

\mathbb {N} } is called arithmetically definable if the graph of f {\displaystyle f} is an arithmetical set. A real number is called arithmetical if the set...

In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain...

about the value, solely within the discourse of real numbers. However, defining the imaginary number i {\displaystyle i} to be equal to − 1 {\displaystyle...

that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D {\displaystyle...

In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer...

In number theory, a number field F is called totally real if for each embedding of F into the complex numbers the image lies inside the real numbers....

measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges...

Real Madrid Club de Fútbol (Spanish pronunciation: [reˈal maˈðɾið ˈkluβ ðe ˈfuðβol] ), commonly referred to as Real Madrid, is a Spanish professional...

mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive...

"Dedekind infinite".) def The set of definable subsets of a set definable A subset of a set is called definable set if it is the collection of elements...

rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits...

values 0, 1 and ∞. The projectively extended real number line is distinct from the affinely extended real number line, in which +∞ and −∞ are distinct. Unlike...

formulas are to definable sets what equations are to varieties over a field. Nonetheless, the interplay of classes of models and the sets definable in them has...

In mathematics, the absolute value or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of...

Real Betis Balompié, known as Real Betis (pronounced [reˈal ˈβetis]) is a Spanish professional football club based in Seville, Andalusia, Spain. It plays...

functions. The theorems of real analysis rely on the properties of the (established) real number system. The real number system consists of an uncountable...

specific real number (which can be identified as the smallest element of the B set). In other words, the number line where every real number is defined as a...