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searching for Cardinality of the continuum 10 found (90 total)

alternate case: cardinality of the continuum

Wetzel's problem (527 words) [view diff] exact match in snippet view article find links to article

asked whether there is a family of analytic functions, with the cardinality of the continuum, such that each complex number has a smaller-than-continuum set

Grothendieck universe (1,277 words) [view diff] exact match in snippet view article find links to article

is any real number, and xα = {xα} for each α. Then U has the cardinality of the continuum, but all of its members have finite cardinality and so c ( U

Function of a real variable (3,560 words) [view diff] exact match in snippet view article find links to article

_{2}=2^{\mathfrak {c}}} , which is strictly larger than the cardinality of the continuum (i.e., set of all real numbers). This fact is easily verified

Zariski tangent space (1,244 words) [view diff] exact match in snippet view article find links to article

{m}}^{2}} is at least the c {\displaystyle {\mathfrak {c}}} , the cardinality of the continuum. The dimension of the Zariski tangent space ( m / m 2 ) ∗ {\displaystyle

Transcendental extension (1,680 words) [view diff] exact match in snippet view article find links to article

transcendental. The transcendence degree of C or R over Q is the cardinality of the continuum. (Since Q is countable, the field Q(S) will have the same cardinality

Basis (linear algebra) (4,730 words) [view diff] exact match in snippet view article

numbers, Hamel bases are uncountable, and have specifically the cardinality of the continuum, which is the cardinal number 2 ℵ 0 {\displaystyle 2^{\aleph

Inner product space (7,305 words) [view diff] exact match in snippet view article find links to article

dimension of K {\displaystyle K} is c , {\displaystyle c,} the cardinality of the continuum, it must be that | F | = c . {\displaystyle |F|=c.} Let L {\displaystyle

Approximately finite-dimensional C*-algebra (3,201 words) [view diff] exact match in snippet view article find links to article

a family of non-isomorphic type III hyperfinite factors with cardinality of the continuum. Today we have a complete classification of hyperfinite factors

Model theory (9,048 words) [view diff] exact match in snippet view article find links to article

2^{\aleph _{0}}} (where 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} is the cardinality of the continuum). A theory of the first type is called unstable, a theory of

Banach space (17,214 words) [view diff] exact match in snippet view article find links to article

the spaces of continuous functions over compact sets of the cardinality of the continuum". (Russian) Teor. Funkciĭ Funkcional. Anal. i Priložen. Vyp.