In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...

In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance...

into Cardinal and Ordinal Numbers (1958, 2nd ed. 1965). Any finite natural number can be used in at least two ways: as an ordinal and as a cardinal....

have the same ordinal number. The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural...

Continuing in this manner, it is possible to define a cardinal number ℵα for every ordinal number α, as described below. The concept and notation are due to...

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...

arbitrary numerical scale Ordinal date, a simple form of expressing a date using only the year and the day number within that year Ordinal Priority Approach,...

number sign, hash, or pound sign. The symbol has historically been used for a wide range of purposes including the designation of an ordinal number and...

the von Neumann representation of ordinals. Larger ordinal fixed points of the exponential map are indexed by ordinal subscripts, resulting in ε 1 , ε...

limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less...

An ordinal date is a calendar date typically consisting of a year and an ordinal number, ranging between 1 and 366 (starting on January 1), representing...

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

numbers are indexed by ordinal numbers. If the axiom of choice is true, this transfinite sequence includes every cardinal number. If the axiom of choice...

an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal. The ordinals 1...

uncountable ordinal, traditionally denoted by ω 1 {\displaystyle \omega _{1}} or sometimes by Ω {\displaystyle \Omega } , is the smallest ordinal number that...

to distinguish monarchs. An ordinal is the number placed after a monarch's regnal name to differentiate between a number of kings, queens or princes reigning...

The surreal number ω − 1 is not an ordinal; the ordinal ω is not the successor of any ordinal. This is a surreal number with birthday ω + 1, which is labeled...

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are...

smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the empty set is zero, and every ordinal has a rank...

one", "one hundred one" / "a hundred one", and "one oh one". As an ordinal number, 101st (one hundred [and] first), rather than 101th, is the correct...

library ordinal. A byte value that is 0x1X sets the link library ordinal number. The hex digit that is X is a 0 to 15 library ordinal number. A byte value...

zero-based numbering, the initial element is sometimes termed the zeroth element, rather than the first element; zeroth is a coined ordinal number corresponding...

symbols Japanese punctuation Korean punctuation Ordinal indicator – Character(s) following an ordinal number (used of the style 1st, 2nd, 3rd, 4th or as superscript...

assignment that uses ordinal numbers. For a well-orderable set U, we define its cardinal number to be the smallest ordinal number equinumerous to U, using...

Hartogs number is an ordinal number associated with a set. In particular, if X is any set, then the Hartogs number of X is the least ordinal α such that...

theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any β , γ < α {\displaystyle \beta...

thereby assigning it 0 elements. Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order...

to find the ordinal number of a particular object, or to find the object with a particular ordinal number, corresponds to assigning ordinal numbers one...

system of ranks or steps. The number of the rank in question was indicated by ordinal numbers, in abbreviation with the ordinal indicator (a superscript o)...

described by an ordinal number. For instance, 3 is the ordinal number of the set {0, 1, 2} with the usual order 0 < 1 < 2; and ω is the ordinal number of the set...