Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Ordinal arithmetic and Ordinal number

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

Difference between Ordinal arithmetic and Ordinal number

Ordinal arithmetic vs. Ordinal number

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. 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 Ordinal arithmetic and Ordinal number

Ordinal arithmetic and Ordinal number have 12 things in common (in Unionpedia): Additively indecomposable ordinal, Epsilon numbers (mathematics), First uncountable ordinal, Limit ordinal, Natural number, Nimber, Order type, Peano axioms, Set theory, Successor ordinal, Transfinite induction, Well-order.

Additively indecomposable ordinal

In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any \beta,\gamma, we have \beta+\gamma Additively indecomposable ordinals are also called gamma numbers.

Additively indecomposable ordinal and Ordinal arithmetic · Additively indecomposable ordinal and Ordinal number · See more »

Epsilon numbers (mathematics)

In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map.

Epsilon numbers (mathematics) and Ordinal arithmetic · Epsilon numbers (mathematics) and Ordinal number · See more »

First uncountable ordinal

In mathematics, the first uncountable ordinal, traditionally denoted by ω1 or sometimes by Ω, is the smallest ordinal number that, considered as a set, is uncountable.

First uncountable ordinal and Ordinal arithmetic · First uncountable ordinal and Ordinal number · See more »

Limit ordinal

In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal.

Limit ordinal and Ordinal arithmetic · Limit ordinal and Ordinal number · See more »

Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

Natural number and Ordinal arithmetic · Natural number and Ordinal number · See more »

Nimber

In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim.

Nimber and Ordinal arithmetic · Nimber and Ordinal number · See more »

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).

Order type and Ordinal arithmetic · Order type and Ordinal number · See more »

Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

Ordinal arithmetic and Peano axioms · Ordinal number and Peano axioms · See more »

Set theory

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

Ordinal arithmetic and Set theory · Ordinal number and Set theory · See more »

Successor ordinal

In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α.

Ordinal arithmetic and Successor ordinal · Ordinal number and Successor ordinal · See more »

Transfinite induction

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.

Ordinal arithmetic and Transfinite induction · Ordinal number and Transfinite induction · 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.

Ordinal arithmetic and Well-order · Ordinal number and Well-order · See more »

The list above answers the following questions

Ordinal arithmetic and Ordinal number Comparison

Ordinal arithmetic has 44 relations, while Ordinal number has 83. As they have in common 12, the Jaccard index is 9.45% = 12 / (44 + 83).

References

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

Hey! We are on Facebook now! »