Ordinal numeral in the context of "John Paul I"

In linguistics, a numeral in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective. Some theories consider "numeral" to be a synonym for "number" and assign all numbers (including ordinal numbers like "first") to a part of speech called "numerals". Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a pronoun ("the two went to town"), or for a small number of words as an adverb ("I rode the slide twice").

Numerals can express relationships like quantity (cardinal numbers), sequence (ordinal numbers), frequency (once, twice), and part (fraction).

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard bold ⁠${\displaystyle \mathbb {N} }$⁠.

The natural numbers are used for counting, and for labeling the result of a count, like "there are seven days in a week", in which case they are called cardinal numbers. They are also used to label places in an ordered series, like "the third day of the month", in which case they are called ordinal numbers. Natural numbers may also be used to label, like the jersey numbers of a sports team; in this case, they have no specific mathematical properties and are called nominal numbers.

The Earthly Branches (also called the Terrestrial Branches or the 12-cycle) are a system of twelve ordered symbols used throughout East Asia. They are indigenous to China, and are themselves Chinese characters, corresponding to words with no concrete meaning other than the associated branch's ordinal position in the list.

Cultural applications of the Branches include a dating system known as the sexagenary cycle, and their use in Chinese astrology. They are associated with the ten Heavenly Stems in Chinese calendars, and in Taoist practice.

In mathematics, an nth root of a number x is a number r which, when raised to the power of n, yields x: $${\displaystyle r^{n}=\underbrace {r\times r\times \dotsb \times r} _{n{\text{ factors}}}=x.}$$ The positive integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an nth root is a root extraction.

The nth root of x is written as ${\displaystyle {\sqrt[{n}]{x}}}$ using the radical symbol ${\displaystyle {\sqrt {\phantom {x}}}}$. The square root is usually written as ⁠${\displaystyle {\sqrt {x}}}$⁠, with the degree omitted. Taking the nth root of a number, for fixed ⁠${\displaystyle n}$⁠, is the inverse of raising a number to the nth power, and can be written as a fractional exponent:

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

A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used. To extend this process to various infinite sets, ordinal numbers are defined more generally using linearly ordered Greek letter variables that include the natural numbers and have the property that every set of ordinals has a least or "smallest" element (this is needed for giving a meaning to "the least unused element"). This more general definition allows us to define an ordinal number ${\displaystyle \omega }$ (omega) to be the least element that is greater than every natural number, along with ordinal numbers ⁠${\displaystyle \omega +1}$⁠, ⁠${\displaystyle \omega +2}$⁠, etc., which are even greater than ⁠${\displaystyle \omega }$⁠.

In linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count.

Examples in English are the words one, two, three, and the compounds three hundred [and] forty-two and nine hundred [and] sixty. Cardinal numerals are classified as definite, and are related to ordinal numbers, such as the English first, second, third, etc.