What are all the ways you can modify the base "number" concept in a language?

Question

I can think of these examples of numbers, but maybe there are more?

one,two,three
single,double,triple
first,second,third
primary,secondary,tertiary
,couple,triplet

How should I think of these, how do they relate to each other? In my conlang like I have mentioned, I have a base word and then append -i for verbs, -a for nouns, and -u for adjectives/features. Say the base concept of "one" is zen. One sounds like it would be a noun to me, so zena. First is a modifier/feature so it gets the -u, zenu. A single can be like a "single" (single shot at a coffee shop, so a noun or an adjective?) But so now we have let's say 2 adjective forms. Same with primary, so that is 3 adjective forms. So I'm unsure how to fit this into my pattern, and not sure if there is even more I should be aware of.

How do other languages handle these situations? Do they add extra words perhaps (for isolating languages)? If so, what is an example? I feel like I must have to add a particle or modifying word to some of these to make it a differently scoped adjective in the other cases, but it's hard to pinpoint how they are different.

Answer 1

Traditional grammar usually talks about four types: cardinal ("one"), ordinal ("first"), distributive ("one by one"), and adverbial ("once"). These are, not coincidentally, the four types of numbers that are distinguished in Latin morphology: ūnus, prīmus, singulī, and semel respectively. The first three are all adjectives, the fourth is an adverb.

But of course these aren't the only options. Even in Latin you also have the "multiplier" numbers, like simplex "single" and duplex "double", which are traditionally not grouped in with the other numbers. Or you could talk about fractions, like "half" and "third". English has two separate series of ordinals, one from Germanic and one from Latin, with slightly different meanings: "first" versus "primary".

English generally uses different words for each of these classes, but Swahili for example has a much more regular system. Swahili just has one* word for each number, the cardinal: mtoto mtatu "three children". To make the ordinal, you use the associative marker -a: mtoto wa tatu "third child", literally "child of three". For the other constructions where English and Latin have special words, just attach the number to a different noun: mara tatu "thrice", literally "three times"; mara tatu zaidi "triple", literally "three times more"; sehemu ya tatu "one-third", literally "(one) portion of three".

* Well not perfectly regular, because natural languages never are. "First" has a special form, kwanza, derived from the verb "begin"; "two" has a special form, pili, used in counting. But these are the only exceptions I know of.