Search results
Results from the WOW.Com Content Network
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [1]
Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...
Pages in category "Ordinal numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...
The numero sign or numero symbol, № (also represented as Nº, No̱, №, No., or no.), [1] [2] is a typographic abbreviation of the word number(s) indicating ordinal numeration, especially in names and titles. For example, using the numero sign, the written long-form of the address "Number 29 Acacia Road" is shortened to "№ 29 Acacia Rd ...
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion .
In written languages, an ordinal indicator is a character, or group of characters, following a numeral denoting that it is an ordinal number, rather than a cardinal number. Historically these letters were "elevated terminals", that is to say the last few letters of the full word denoting the ordinal form of the number displayed as a superscript .
Every well-ordered set is order-equivalent to exactly one ordinal number, by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. Order types thus often take the form of arithmetic expressions of ordinals.
In fact, the even ordinal ω + 4 cannot be expressed as β + β, and the ordinal number (ω + 3)2 = (ω + 3) + (ω + 3) = ω + (3 + ω) + 3 = ω + ω + 3 = ω2 + 3. is not even. A simple application of ordinal parity is the idempotence law for cardinal addition (given the well-ordering theorem). Given an infinite cardinal κ, or generally any ...