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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, chronology, and so on (e.g., "third", "tertiary"). They differ from cardinal numerals, which represent quantity (e.g., "three") and other types of numerals.
If α is any ordinal and X is a set, an α-indexed sequence of elements of X is a function from α to X. This concept, a transfinite sequence (if α is infinite) or ordinal-indexed sequence, is a generalization of the concept of a sequence. An ordinary sequence corresponds to the case α = ω, while a finite α corresponds to a tuple, a.k.a ...
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Ordinal Priority Approach, a multiple-criteria decision analysis method that aids in solving the group decision-making problems; Ordinal indicator, the sign adjacent to a numeral denoting that it is an ordinal number; Ordinal number in set theory, a number type with order structures; Ordinal number (linguistics), a word representing the rank of ...
The ordinal catgegory are based on ordinal numbers such as the English first, second, third, which specify position of items in a sequence. 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.
Exception to this rule are the ordinal numerals first, second and third. If the basic word ends on the letter t and we add the suffixes for ordinal numerals, then a double t is generally produced. For the ordinal numerals seventh and eighth, we reduce some of the letters of the basic number, for example: osum > osmi (eighth), sedum > sedmi ...
This set is ordered lexicographically with the least significant position first: we write f < g if and only if there exists x ∈ β with f(x) < g(x) and f(y) = g(y) for all y ∈ β with x < y. This is a well-ordering and hence gives an ordinal number. The definition of exponentiation can also be given by transfinite recursion on the exponent β.
Buchholz (1986) described the following system of ordinal notation as a simplification of Feferman's theta functions. Define: Ω ξ = ω ξ if ξ > 0, Ω 0 = 1; The functions ψ v (α) for α an ordinal, v an ordinal at most ω, are defined by induction on α as follows: ψ v (α) is the smallest ordinal not in C v (α)