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Burali-Forti paradox and Ordinal number

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Burali-Forti paradox and Ordinal number

Burali-Forti paradox vs. Ordinal number

In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.

Similarities between Burali-Forti paradox and Ordinal number

Burali-Forti paradox and Ordinal number have 8 things in common (in Unionpedia): Historia Mathematica, John von Neumann, New Foundations, Order type, Set theory, Transitive set, Well-order, Zermelo–Fraenkel set theory.

Historia Mathematica

Historia Mathematica: International Journal of History of Mathematics is an academic journal on the history of mathematics published by Elsevier.

Burali-Forti paradox and Historia Mathematica · Historia Mathematica and Ordinal number · See more »

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.

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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.

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Order type

In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order).

Burali-Forti paradox and Order type · Order type and Ordinal number · See more »

Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

Burali-Forti paradox and Set theory · Ordinal number and Set theory · See more »

Transitive set

In set theory, a set A is called transitive if either of the following equivalent conditions hold.

Burali-Forti paradox and Transitive set · Ordinal number and Transitive set · See more »

Well-order

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.

Burali-Forti paradox and Well-order · Ordinal number and Well-order · See more »

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.

Burali-Forti paradox and Zermelo–Fraenkel set theory · Ordinal number and Zermelo–Fraenkel set theory · See more »

The list above answers the following questions

Burali-Forti paradox and Ordinal number Comparison

Burali-Forti paradox has 22 relations, while Ordinal number has 83. As they have in common 8, the Jaccard index is 7.62% = 8 / (22 + 83).

References

This article shows the relationship between Burali-Forti paradox and Ordinal number. To access each article from which the information was extracted, please visit:

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