English Dictionary

ordinal number

noun

(grammar) A word that expresses the relative position of an item in a sequence. / (arithmetic) A natural number used to denote position in a sequence.

She won the first place in the competition.

意味（1）

(grammar) A word that expresses the relative position of an item in a sequence.

First, second and third are the ordinal numbers corresponding to one, two and three.

意味（2）

(arithmetic) A natural number used to denote position in a sequence.

In the expression a₃, the 3 is an ordinal number.

意味（3）

(set theory) Such a number generalised to correspond to any cardinal number (the size of some set); formally, the order type of some well-ordered set of some cardinality a, which represents an equivalence class of well-ordered sets (exactly those of cardinality a) under the equivalence relation "existence of an order-preserving bijection".

For not only do the antinomies a) to e) disappear when we admit as elements of sets only such sets, ordinal numbers, and cardinal numbers as are bounded above by a fixed cardinal number, but we see also that paradoxes always arise if we collect into a set any sets, cardinal numbers, or ordinal numbers which are not bounded above by a fixed cardinal number.