Assertion: set | /r/HasProperty | uncountable
Facets:
value: in one model of set theory
type: OTHER
value: countable in a larger model
type: OTHER
Source sentences:
text: Every Vitali set V is uncountable, and v−u is irrational for any u , v ∈ V , u ≠ v {
text: It is possible for a set to be uncountable in one model of set theory but countable in a larger model (because the bijections that establish countability are in the larger model but not the smaller one).
text: The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.
text: The best known example of an uncountable set is the set R of all real numbers; Cantor's diagonal argument shows that this set is uncountable.
text: The diagonalization proof technique can also be used to show that several other sets are uncountable, such as the set of all infinite sequences of natural numbers and the set of all subsets of the set of natural numbers.