How many categories of numerals are there, and what are their functions? No, you haven’t stumbled onto DailyMathTips.com by mistake; this post helps sort out the ways you can refer to numbers and under which circumstances, with nary a digit or operational sign in sight. Ready? One, two, three . . .
1. Cardinal Numbers
Cardinal numbers — one, two, three, or the numeric equivalents, and so on — represent simple quantity (though, as shown in the previous paragraph, they can also be employed in a countdown — or, in that case, a countup). The names of English numerals are all derived from Old English, as are the suffixes -teen, which derives from a form of ten and means “ten more than,” and -ty, which means “ten.” Hundred and thousand are also derived from old English, but million and other terms for orders of magnitude come from Latin by way of French.
2. Collective Numerals
Collective numerals represent sets. There are various subcategories — kinship terms such as twin and triplet, and musical terms like duo and trio – and, well, singletons, like that word, pair, dozen, and so on. Language origin varies among these assorted words.
3. Composite Numbers
Composite numbers — unary, binary, ternary, and so on — represent composition (what something is composed of). Binary is the only one of these Latin-derived terms commonly used, though quaternary was applied to a geological age.
4. Distributive Numerals
Distributive numerals represent alternating patterns. In some languages (like Latin, which has singuli and bini, for example, to mean “one by one” or “two by two” respectively), these numerals are represented by a single term, are usually described in English in phrases such as “each day,” “every other week,” and “every third month.” However, English also has one-word examples such as centennial and its multiplied variants, descended from Latin terms.
5. Multiplicative Numbers
Multiplicative numbers — once, twice, thrice — represent repetition. The ancestors of these words are variations on the Old English words for one, two, and three. Among the categories listed in this post, the multiplicative group is the only one that does not represent any value higher than three. (The reason for this lack is unknown, though perhaps it’s because it’s rarely necessary to describe an attempt or action beyond several previous efforts.)
6. Ordinal Numbers
Ordinal numbers — first, second, third, and so on — represent sequential order. Second is anomalous in that it alone comes from Latin rather than Old English; it supplanted the ambiguous English word other (still used in this sense in the phrase “every other”). There was never a twoth — or a onth, for that matter; that latter vacancy was filled by a form of fore, while third and so on are derived from the cardinal numbers.)
This is a good place to remind writers to deactivate the function on their computer that, by default, creates superscript ordinal indicators (miniature renditions of st, nd, rd, and th perched on the right shoulders of numerals). The perverse persistence of this Victorian affectation in state-of-the-art word-processing programs is a puzzler — and an annoyance to editors, who have to convert such aberrant symbols into baseline indicators before production.
7. Partitive Numbers
Partitive numbers — half, thirds, fourths, and so on — represent fractions. Half, which is from Old English, originally meant merely “part.” (Behalf, meaning “on the part of,” retains this imprecise meaning.) The others are just variations on Old English terms for the associated numbers.
8. Ranking Numerals
Ranking numerals – primary, secondary, tertiary, and so on (this class shares quaternary and higher values with the composite-numbers category) — represent degrees of importance or relevance. These terms are ultimately Latin in origin.
9. Reproductive Numbers
Reproductive numbers — single, double, triple, and so on, plus the generic multiple — represent replication. Single and double are from Latin by way of French; the higher values are all directly from Latin.
10. Miscellaneous Terms
Deuce, from the similarly pronounced precursor to French deux, is an old-fashioned synonym for two that persists in sports and gambling references. The mild oath “What the deuce,” a euphemism for “What the devil?” probably comes from association with deuce as a low score and therefore the outcome of bad luck.
Trinity, from Latin through French, and triad, directly from Latin, both mean “a group or set of three.” Triplicate, meaning “threefold,” is from Latin; -fold is from the Old English cognate of -plus, which is where we got the element -ple and its extension -plicate. Treble is the French form of triple; both come from the Latin triplus. Trice, used in the phrase “in a trice,” meaning “quickly,” is unrelated to thrice (“three times”); it’s of nautical origin, from a Middle English word borrowed from a Dutch term meaning “pull, hoist.”
Huh, I suppose this is what I get for not paying attention in school. I knew some of these, but it is still good to see it all laid out in front of me. Thanks for sharing this, glad you did!
Nicely done, Mark!
I have noticed that ‘once,’ ‘twice’ and ‘thrice’ are more frequently being replaced by ‘one time,’ ‘two times’ and ‘three times.’
I might simply put this down to regularization by analogy with ‘four times’ etc. However, since the usage seems to be spreading from US sources, I am led to suspect a Midwestern-style loan-translation from German ‘einmal,’ ‘zweimal’ and ‘dreimal.’
Interestingly, the usage requires a syntactic adjustment – one says “twice as fast as” but “two times faster than.”