Countable Corporation (aka Countable) is a Software-as-a-Service (SaaS) company based in San Francisco. The company was founded in 2013 by its CEO Bart...

is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if...

topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base. More explicitly...

support from other users. In 2019, Causes was acquired by Countable Corporation. In 2020, Countable.us and its associated app merged with Causes.com. Causes...

requirements: First, the probability of a countable union of mutually exclusive events must be equal to the countable sum of the probabilities of each of these...

collection of things. One is most commonly a determiner used with singular countable nouns, as in one day at a time. The determiner has two senses: numerical...

I}X_{i}} is not empty. The union of any countable family of countable sets is countable (this requires countable choice but not the full axiom of choice)...

of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps...

Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included...

a pair, and no object is paired more than once (see image). A set is countably infinite if it can be placed in one-to-one correspondence with the set...

informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number:...

with Cartesian coordinates in classical geometry. When this basis is countably infinite, it allows identifying the Hilbert space with the space of the...

[0,ω1] is not first-countable. The subspace [0,ω1) is first-countable however, since the only point in [0,ω1] without a countable local base is ω1. Some...

commonly used as a mass noun ("some Lego") or, in American English, as a countable noun with plural "Legos", to refer to the bricks themselves, but as is...

subsets of X {\displaystyle X} whose complements in X {\displaystyle X} are countable. Cofinite topology Double-pointed cofinite topology Ordinal number topology...

by Pinterest. The remaining company assets and IP, including the Causes assets, were purchased by GovTech app Countable. James Windon was the president...

known about infinitely generated abelian groups, even in the torsion-free countable case. An abelian group ⟨ G , + , 0 ⟩ {\displaystyle \langle G,+,0\rangle...

uncountable set of disjoint copies into three-dimensional space, only a countable number of Möbius strips can be simultaneously embedded. A path along the...

W=\bigcup _{n<\omega }\{w\in W:|w|<n\}} would be a countable union of countable sets, thus countable). If p ( e 1 ) = b 1 {\displaystyle p(e_{1})=b_{1}}...

≥ 2 by choosing the domain as { 0, 1/(n − 1), 2/(n − 1), ..., 1 } any countable set by choosing the domain as { p/q | 0 ≤ p ≤ q where p is a non-negative...

Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational. The first proof...

motivate the mean field simulation algorithm we start with S a finite or countable state space and let P(S) denote the set of all probability measures on...

can only have jump discontinuities; f {\displaystyle f} can only have countably many discontinuities in its domain. The discontinuities, however, do not...

closed category, a concept in category theory CCC, Roman numeral for 300 Countable chain condition, in order theory CCCn, cube-connected cycles of order...

{\displaystyle |\mathbb {N} |=\aleph _{0}} are called countable sets; these are either finite sets or countably infinite sets (sets of cardinality ℵ 0 {\displaystyle...

precise sense described herein. In particular, the concept applies to countable families, and thus sequences of functions. Equicontinuity appears in the...

can be expressed as the sum of five non-zero squares. There are five countably infinite Ramsey classes of permutations.: p.4  5 is conjectured to be...

well-ordered countably infinite set without limit points. This assignment can be generalized to general well-orderings with a cardinality beyond countability, to...

Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included...

( x ) {\displaystyle x\in f(x)} ", this is a diagonal argument. For a countable (or finite) set, the argument of the proof given above can be illustrated...