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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 ] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
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 ...
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
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 .
In Latin and Greek, the ordinal forms are also used for fractions for amounts higher than 2; only the fraction 1 / 2 has special forms. The same suffix may be used with more than one category of number, as for example the orginary numbers second ary and terti ary and the distributive numbers bi nary and ter nary .
A Gödel numbering is a function mapping the set of well-formed formulae (a finite sequence of symbols on which the ordinal notation function is defined) of some formal language to the natural numbers. This associates each well-formed formula with a unique natural number, called its Gödel number.
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 ...
To define ℵ α for arbitrary ordinal number α, we must define the successor cardinal operation, which assigns to any cardinal number ρ the next larger well-ordered cardinal ρ + (if the axiom of choice holds, this is the (unique) next larger cardinal). We can then define the aleph numbers as follows: ℵ 0 = ω ℵ α+1 = (ℵ α) +