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SUBCOUNTABILITY

Subcountability

Mathematical property of sets

unconditionally impossible. We conclude that the subcountability axiom, asserting all sets are subcountable, is incompatible with P N {\displaystyle {\mathcal

Subcountability

Cantor's diagonal argument

Proof in set theory

axiom of powerset is not adopted, in a constructive framework even the subcountability of all sets is then consistent. That all said, in common set theories

Cantor's diagonal argument

Cantor's_diagonal_argument

Constructive set theory

Axiomatic set theories based on the principles of mathematical constructivism

Markovian school is the permitted subcountability of various uncountable collections. When adopting the subcountability of the collection of all unending

Constructive set theory

Constructive_set_theory

Cardinality

Size of a set in mathematics

Multiplicity (mathematics) Natural density Numerosity (mathematics) Subcountability The actually-infinite set of natural numbers is guaranteed to exist

Cardinality

Computable number

Real number that can be computed within arbitrary precision

countably many Turing machines, showing that the computable numbers are subcountable. The set S {\displaystyle S} of these Gödel numbers, however, is not

Computable number

Computable_number

Subquotient

Group-theoretic concept

{\displaystyle \leq } on corresponding cardinals. Homological algebra Subcountable Griess, Robert L. (1982), "The Friendly Giant", Inventiones Mathematicae

Subquotient

Constructive analysis

Mathematical analysis

{Q} }^{\mathbb {N} }} or some models of the reals can be taken to be subcountable. That said, Cantors diagonal construction proving uncountability of powersets

Constructive analysis

Constructive_analysis