## Chapter 18: lojbau mekso: Mathematical Expressions in Lojban

_{19. Other uses of mekso}

_{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, ...}

_{f or as many places as may be required. For example:}

_{✥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.}