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Ordinal Number. In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal number (sometimes simply called an ordinal for short) is one of the numbers in Georg Cantor's extension of the whole numbers. An ordinal number is defined as the order type of a well ordered set (Dauben 1990, p. 199; Moore 1982, p. 52; Suppes 1972, p. 129).
1 When using number words, it is important to keep the difference between cardinal numbers and ordinal numbers in mind. 2  Cardinal numbers are counting numbers. 3  They express absolute number without any implication of position. . . . 4 The ordinal numbers, on the other hand, are position numbers.y Richard Nordquist. Definition: A number (such as 1, 2, or 3) used in counting to indicate quantity but not order. Though not all style guides agree, the general rule is that cardinal numbers one through nine are spelled out, numbers 10 and above are written in figures.