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Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced.
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.
The ordinal category 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.
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) +
In English, superior letters are reserved for use with ordinal numerals, as in 1st, 2nd, 3rd, etc. However, this use is not mandatory and not always preferred: 1st, 2nd, 3rd, etc. are also accepted abbreviations of ordinal numerals. Previously, in English-speaking countries, abbreviations of given names were used for recordkeeping. Today, their ...
The ampersand (&) has sometimes appeared at the end of the English alphabet, as in Byrhtferð's list of letters in 1011. [2] & was regarded as the 27th letter of the English alphabet, as taught to children in the US and elsewhere. [vague] An example may be seen in M. B. Moore's 1863 book The Dixie Primer, for the Little Folks. [3]
The ξ-notations can be used to name any ordinal less than ε 0 with an alphabet of only two symbols ("0" and "ξ"). If these notations are extended by adding functions that enumerate epsilon numbers, then they will be able to name any ordinal less than the first epsilon number that cannot be named by the added functions.
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 .
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