Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
The following cmavo are discussed in this section:
ro PA all so'a PA almost all so'e PA most so'i PA many so'o PA several so'u PA a few no'o PA the typical number of da'a PA all but (one) of piro PA+PA the whole of/all of piso'a PA+PA almost the whole of piso'e PA+PA most of piso'i PA+PA much of piso'o PA+PA a small part of piso'u PA+PA a tiny part of pino'o PA+PA the typical portion of rau PA enough du'e PA too many mo'a PA too few pirau PA+PA enough of pidu'e PA+PA too much of pimo'a PA+PA too little of
Not all the cmavo of PA represent numbers in the usual mathematical sense. For example, the cmavo “ro” means “all” or “each”. This number does not have a definite value in the abstract: “li ro” is undefined. But when used to count or quantify something, the parallel between “ro” and “pa” is clearer:
The cmavo “so'a”, “so'e”, “so'i”, “so'o”, and “so'u” represent a set of indefinite numbers less than “ro”. As you go down an alphabetical list, the magnitude decreases:
✥8.3 mi catlu so'a prenu I look-at almost-all persons ✥8.4 mi catlu so'e prenu I look-at most persons ✥8.5 mi catlu so'i prenu I look-at many persons ✥8.6 mi catlu so'o prenu I look-at several persons ✥8.7 mi catlu so'u prenu I look-at a-few persons
The English equivalents are only rough: the cmavo provide space for up to five indefinite numbers between “ro” and “no”, with a built-in ordering. In particular, “so'e” does not mean “most” in the sense of “a majority” or “more than half”.
Each of these numbers, plus “ro”, may be prefixed with “pi” (the decimal point) in order to make a fractional form which represents part of a whole rather than some elements of a totality. “piro” therefore means “the whole of”:
✥8.8 mi citka piro lei nanba I eat the-whole-of the-mass-of bread
Similarly, “piso'a” means “almost the whole of”; and so on down to “piso'u”, “a tiny part of”. These numbers are particularly appropriate with masses, which are usually measured rather than counted, as ✥8.8 shows.
In addition to these cmavo, there is “no'o”, meaning “the typical value”, and “pino'o”, meaning “the typical portion”: Sometimes “no'o” can be translated “the average value”, but the average in question is not, in general, a mathematical mean, median, or mode; these would be more appropriately represented by operators.
✥8.9 mi catlu no'o prenu I look-at a-typical-number-of persons ✥8.10 mi citka pino'o lei nanba I eat a-typical-amount-of the-mass-of bread.
“da'a” is a related cmavo meaning “all but”:
✥8.11 mi catlu da'a re prenu I look-at all-but two persons ✥8.12 mi catlu da'a so'u prenu I look-at all-but a-few persons
If no number follows “da'a”, then “pa” is assumed; “da'a” by itself means “all but one”, or in ordinal contexts “all but the last”:
✥8.13 ro ratcu ka'e citka da'a ratcu all rats can eat all-but-one rats. All rats can eat all other rats.
(The use of “da'a” means that ✥8.13 does not require that all rats can eat themselves, but does allow it. Each rat has one rat it cannot eat, but that one might be some rat other than itself. Context often dictates that “itself” is, indeed, the “other” rat.)
As mentioned in c18-§3, “ma'u” and “ni'u” are also legal numbers, and they mean “some positive number” and “some negative number” respectively.
✥8.14 li ci vu'u re du li ma'u the-number 3 - 2 = some-positive-number ✥8.15 li ci vu'u vo du li ni'u the-number 3 - 4 = some-negative-number ✥8.16 mi ponse ma'u rupnu I possess a-positive-number-of currency-units.
All of the numbers discussed so far are objective, even if indefinite. If there are exactly six superpowers (“rairgugde”, “superlative-states”) in the world, then “ro rairgugde” means the same as “xa rairgugde”. It is often useful, however, to express subjective indefinite values. The cmavo “rau” (enough), “du'e” (too many), and “mo'a” (too few) are then appropriate:
✥8.17 mi ponse rau rupnu I possess enough currency-units.
Like the “so'a”-series, “rau”, “du'e”, and “mo'a” can be preceded by “pi”; for example, “pirau” means “a sufficient part of.”
Another possibility is that of combining definite and indefinite numbers into a single number. This usage implies that the two kinds of numbers have the same value in the given context:
✥8.18 mi viska le rore gerku I saw the all-of/two dogs. I saw both dogs. ✥8.19 mi speni so'ici prenu I am-married-to many/three persons. I am married to three persons (which is “many” in the circumstances).
✥8.19 assumes a mostly monogamous culture by stating that three is “many”.