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In the sentence "He was number three to finish the race", is the word "three" an ordinal or cardinal number?

My gut reaction is that it's a cardinal number, but I'm having a hard time arguing for it.

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    Grammatically, it's definitely a cardinal order. Mathematically, you could call it an ordinal number. (Mathematically, cardinal numbers tell how many things there are while ordinal numbers tell what position things are in.) – Peter Shor Dec 12 '14 at 13:20
  • @PeterShor, I see the distinction ... I'd just prefer it to be a more clear-cut, universal demarcation. – Tarjei Dec 12 '14 at 13:46
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I've revised and extended my original answer.

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... Weisstein, Eric W. "Cardinal Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CardinalNumber.html

… [A]n ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. (Weisstein, Eric W. "Ordinal Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinalNumber.html)

The number, “three", is cardinal and "third" is ordinal. Nonetheless, in the sentence, "He was number three to finish the race", ordinal numbers merit some attention.

Imagine a collection of runners at the finish line, discussing the results of the race.

One runner says, " I was number three to finish the race".

Another says, "I was number two."

Still another runner says, "I was number one"

These runners are discussing their ranks, that is, the order in which they crossed the finish line. They are not discussing how many runners are in a set.

Cardinal numbers are being employed to assign positions to runners along an ordering. This is possible because the cardinal numbers are themselves ordered.

For the case at hand, the cardinal number three is being used as a “figure of speech” (https://en.wikipedia.org/wiki/Figure_of_speech) for the ordinal number, “third”.

  • Have you an authority demanding that function rather than form is primary in defining the term 'cardinal number'? – Edwin Ashworth Sep 5 '15 at 14:18
  • Fair point. I've since revised my answer in a way that does not require favouring one criterion over the other. – DavidC Sep 5 '15 at 15:28
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Cardinal.

I always think that ordinal numbers tell what order something happened in: first, second, third...

But we don't use the construction "number second* for anything. It's always "number [cardinal]."

  • Thank you. I just find it strange that they seem to serve the same purpose in the sentence, namely giving the order of the people finishing the race – Tarjei Dec 12 '14 at 12:19
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    Have you an authority demanding that form rather than function is primary in defining the term 'cardinal number'? – Edwin Ashworth Sep 5 '15 at 14:17
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"Number three" is cardinal. Had you said he was the third to finish the race", "third" would be ordinal.

"Three", as far as i know, is always cardinal.

  • "Three", taken alone and out of context, is indeed cardinal. However, the word is being used in an unusual, ordinal sense in the given sentence. – DavidC Sep 5 '15 at 14:11
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    Have you an authority demanding that form rather than function is primary in defining the term 'cardinal number'? – Edwin Ashworth Sep 5 '15 at 14:18

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