Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
The following cmavo are discussed in this section:
me'o LI the mekso nu'a NUhA operator to selbri mai MAI utterance ordinal mo'o MAI higher order utterance ordinal roi ROI quantified tense
So far we have seen mekso used as sumti (with “li”), as quantifiers (often parenthesized), and in MOI and ME-MOI selbri. There are a few other minor uses of mekso within Lojban.
The cmavo “me'o” has the same grammatical use as “li” but slightly different semantics. “li” means “the number which is the value of the mekso ...”, whereas “me'o” just means “the mekso ...” So it is true that:
✥19.1 li re su'i re du li vo the-number two plus two equals the-number four 2 + 2 = 4
but false that:
✥19.2 me'o re su'i re du me'o vo the-mekso two plus two equals the-mekso four “2 + 2” = “4”
since the expressions “2 + 2” and “4” are not the same. The relationship between “li” and “me'o” is related to that between “la djan.”, the person named John, and “zo .djan.”, the name “John”.
The cmavo “nu'a” is the inverse of “na'u”, and allows a mekso operator to be used as a normal selbri, with the place structure:
- x1 is the result of applying (operator) to x2, x3, ...
✥19.3 li ni'umu cu nu'a va'a li ma'umu the-number -5 is-the-negation-of the-number +5
uses “nu'a” to make the operator “va'a” into a two-place bridi.
Used together, “nu'a” and “na'u” make it possible to ask questions about mekso operators, even though there is no specific cmavo for an operator question, nor is it grammatical to utter an operator in isolation. Consider ✥19.4, to which ✥19.5 is one correct answer:
✥19.4 li re na'u mo re du li vo the-number two what-operator? two equals the-number four 2 ? 2 = 4 ✥19.5 nu'a su'i plus
In ✥19.4, “na'u mo” is an operator question, because “mo” is the selbri question cmavo and “na'u” makes the selbri into an operator. ✥19.5 makes the true answer “su'i” into a selbri (which is a legal utterance) with the inverse cmavo “nu'a”. Mechanically speaking, inserting ✥19.5 into ✥19.4 produces:
✥19.6 li re na'u nu'a su'i re du li vo the-number two (the-operator the-selbri plus) two equals the-number four
where the “na'u nu'a” cancels out, leaving a truthful bridi.
Numerical free modifiers, corresponding to English “firstly”, “secondly”, and so on, can be created by suffixing a member of selma'o MAI to a digit string or a lerfu string. (Digit strings are compound cmavo beginning with a cmavo of selma'o PA, and containing only cmavo of PA or BY; lerfu strings begin with a cmavo of selma'o BY, and likewise contain only PA or BY cmavo.) Here are some examples:
✥19.7 pamai firstly ✥19.8 remai secondly ✥19.9 romai all-ly lastly ✥19.10 ny.mai nth-ly ✥19.11 pasomo'o nineteenthly (higher order) c18-§19
The difference between “mai” and “mo'o” is that “mo'o” enumerates larger subdivisions of a text. Each “mo'o” subdivision can then be divided into pieces and internally numbered with “mai”. If this chapter were translated into Lojban, it would number each section with “mo'o”.
A numerical tense can be created by suffixing a digit string with “roi”. This usage generates tenses corresponding to English “once”, “twice”, and so on. This topic belongs to a detailed discussion of Lojban tenses, and is explained further in Chapter 10.
Note: the elidable terminator “boi” is not used between a number and a member of MAI or ROI.