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Nevertheless, it is deemed unlikely that ZFC harbors an unsuspected contradiction; it is widely believed that if ZFC were inconsistent, that fact would have been uncovered by now. This much is certain — ZFC is immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox.
The collection of countable transitive models of ZFC (in some universe) is called the hyperverse and is very similar to the "multiverse". A typical difference between the universe and multiverse views is the attitude to the continuum hypothesis. In the universe view the continuum hypothesis is a meaningful question that is either true or false ...
An initial segment of the von Neumann universe. Ordinal multiplication is reversed from our usual convention; see Ordinal arithmetic.. The cumulative hierarchy is a collection of sets V α indexed by the class of ordinal numbers; in particular, V α is the set of all sets having ranks less than α.
A federal judge in New York on Friday denied former New Jersey Sen. Robert Menendez's bid for a new trial. "The jury's guilty verdicts were readily supported by the extensive witness testimony and ...
Axiom — For any set X of nonempty sets, there exists a choice function f that is defined on X and maps each set of X to an element of that set. Formally, this may be expressed as follows: ∀ X [ ∅ ∉ X ∃ f : X → ⋃ A ∈ X A ∀ A ∈ X ( f ( A ) ∈ A ) ] . {\displaystyle \forall X\left[\varnothing \notin X\implies \exists f\colon X ...
2. Hoppin’ John. Southerners are usually eating Hoppin’ John (a simmery mix of black-eyed peas and rice) on New Year's Day. Like most “vegetable” recipes from around this area, it contains ...
Wikipedia:Maps for Wikipedia, a list of mapping tools available on Wikipedia; Wikipedia:Why mapframe maps?, an essay about mapframe advantages; Wikipedia:Mapframe maps in infoboxes, a project page tracking implementation status; mw:Help:VisualEditor/Maps, documentation for users using the visual editor to edit maps
President-elect Donald Trump charged Elon Musk and former presidential candidate Vivek Ramaswamy with cutting government spending. Years of comments from both men suggest they could aim to do much ...