Similarities between Non-well-founded set theory and Ordinal number
Non-well-founded set theory and Ordinal number have 7 things in common (in Unionpedia): Axiom of regularity, John von Neumann, New Foundations, Set theory, Urelement, Well-founded relation, Zermelo–Fraenkel set theory.
Axiom of regularity
In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.
Axiom of regularity and Non-well-founded set theory · Axiom of regularity and Ordinal number ·
John von Neumann
John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.
John von Neumann and Non-well-founded set theory · John von Neumann and Ordinal number ·
New Foundations
In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica.
New Foundations and Non-well-founded set theory · New Foundations and Ordinal number ·
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
Non-well-founded set theory and Set theory · Ordinal number and Set theory ·
Urelement
In set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object (concrete or abstract) that is not a set, but that may be an element of a set.
Non-well-founded set theory and Urelement · Ordinal number and Urelement ·
Well-founded relation
In mathematics, a binary relation, R, is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.
Non-well-founded set theory and Well-founded relation · Ordinal number and Well-founded relation ·
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
Non-well-founded set theory and Zermelo–Fraenkel set theory · Ordinal number and Zermelo–Fraenkel set theory ·
The list above answers the following questions
- What Non-well-founded set theory and Ordinal number have in common
- What are the similarities between Non-well-founded set theory and Ordinal number
Non-well-founded set theory and Ordinal number Comparison
Non-well-founded set theory has 40 relations, while Ordinal number has 83. As they have in common 7, the Jaccard index is 5.69% = 7 / (40 + 83).
References
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