Definable real number information

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...

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

advanced mathematics, the number line can be called the real line or real number line, formally defined as the set R of all real numbers. It is viewed as...

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...

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

arithmetically definable, but not vice versa. There are many arithmetically definable, noncomputable real numbers, including: any number that encodes the...

\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...

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 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....

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...

compass construction problem put forth by Pappus. Computable number Definable real number Kazarinoff (2003, pp. 10 & 15); Martin (1998), Corollary 2.16...

"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...

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

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

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...

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...

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...

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

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...

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 of finite degree...

property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line. This...

For every real number r, the constant function ( x ) ↦ r {\displaystyle (x)\mapsto r} , is everywhere defined. For every real number r and every function...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers...