Definitions for subcountability
sub·count·abil·i·ty

WiktionaryRate this definition:0.0 / 0 votes

1. subcountabilitynoun

   The property of being subcountable.

WikipediaRate this definition:0.0 / 0 votes

1. Subcountability

   In constructive mathematics, a collection X {\displaystyle X} is subcountable if there exists a partial surjection from the natural numbers onto it. This may be expressed as where f : I ↠ X {\displaystyle f\colon I\twoheadrightarrow X} denotes that f {\displaystyle f} is a surjective function from a I {\displaystyle I} onto X {\displaystyle X} . The surjection is a member of N ⇀ X {\displaystyle {\mathbb {N} }\rightharpoonup X} and here the subclass I {\displaystyle I} of N {\displaystyle {\mathbb {N} }} is required to be a set. In other words, all elements of a subcountable collection X {\displaystyle X} are functionally in the image of an indexing set of counting numbers I ⊆ N {\displaystyle I\subseteq {\mathbb {N} }} and thus the set X {\displaystyle X} can be understood as being dominated by the countable set N {\displaystyle {\mathbb {N} }} . Note that nomenclature of countability and finiteness properties vary substantially, historically. The discussion here concerns the property defined in terms of surjections onto the set in question.

WikidataRate this definition:0.0 / 0 votes

1. Subcountability

   In constructive mathematics, a collection is subcountable if there exists a partial surjection from the natural numbers onto it. The name derives from the intuitive sense that such a collection is "no bigger" than the counting numbers. The concept is trivial in classical set theory, where a set is subcountable if and only if it is finite or countably infinite. Constructively it is consistent to assert the subcountability of some uncountable collections such as the real numbers. Indeed there are models of the constructive set theory CZF in which all sets are subcountable and models of IZF in which all sets with apartness relations are subcountable.

How to pronounce subcountability?

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How to say subcountability in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of subcountability in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of subcountability in Pythagorean Numerology is: 4

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Subcountability
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Subcountability
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=subcountability