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....

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...

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...

possible to define an infinite cardinal number ℵ α {\displaystyle \aleph _{\alpha }} for every ordinal number α , {\displaystyle \alpha ,} as described...

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...

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...

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

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...

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...

been used for a wide range of purposes including the designation of an ordinal number and as a ligatured abbreviation for pounds avoirdupois – having been...

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,...

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

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...

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

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

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

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...

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...

In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers. They are useful in some transfinite...

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...

notation for ordinal weeks of the year. The Gregorian leap cycle, which has 97 leap days spread across 400 years, contains a whole number of weeks (20871)...

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

functions. Chaitin's constant. In set theory, the first uncountable ordinal number, ω1 or Ω The absolute infinite proposed by Georg Cantor. As part of...

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...

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...

registry number, three digits (SSS) as a combination of the citizen's sex and ordinal number of birth, and one digit (C) as a control number. The two...

is not a successor. Transfinite induction is fundamental for defining ordinal numbers and cardinal numbers. Algebra of sets Alternative set theory Category...