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

_{21. Miscellany}

_{A few other points:}

_{“se” can be used to convert an operator as if it were
a selbri, so that its arguments are exchanged. For
example:}

_{✥21.1 li ci se vu'u vo du li pa the-number three (inverse) minus four equals the-number one. 3 subtracted from 4 equals 1. }

_{The other converters of selma'o SE can also be used on
operators with more than two operands, and they can be
compounded to create (probably unintelligible) operators as
needed.}

_{Members of selma'o NAhE are also legal on an operator
to produce a scalar negation of it. The implication is that
some other operator would apply to make the bridi
true:}

_{✥21.2 li ci na'e su'i vo du li pare the-number 3 non-plus 4 equals the-number 12 }

_{✥21.3 li ci to'e vu'u re du li mu the-number 3 opposite-of-minus 2 equals the-number 5 }

_{The sense in which “plus” is the opposite of
“minus” is not a mathematical but rather a linguistic one;
negated operators are defined only loosely.}

_{“la'e” and “lu'e” can be used on operands with the
usual semantics to get the referent of or a symbol for an
operand. Likewise, a member of selma'o NAhE followed by “bo”
serves to scalar-negate an operand, implying that some other
operand would make the bridi true:}

_{✥21.4 li re su'i re du li na'ebo mu the-number 2 plus 2 equals the-number non-5. 2 + 2 ⇔ something other than 5. }

_{The digits 0-9 have rafsi, and therefore can be used in
making lujvo. Additionally, all the rafsi have CVC form and can
stand alone or together as names:}

_{✥21.5 la zel. poi gunta la tebes. pu nanmu those-named “Seven” who attack that-named “Thebes” [past] are-men The Seven Against Thebes were men. }

_{Of course, there is no guarantee that the name “zel.”
is connected with the number rafsi: an alternative which cannot
be misconstrued is:}

_{✥21.6 la zemei poi gunta la tebes. pu nanmu those-named-the Sevensome who attack Thebes [past] are-men. }

_{Certain other members of PA also have assigned rafsi:
“so'a”, “so'e”, “so'i”, “so'o”, “so'u”, “da'a”,
“ro”, “su'e”, “su'o”, “pi”, and “ce'i”. Furthermore,
although the cmavo “fi'u” does not have a rafsi as such, it
is closely related to the gismu “frinu”, meaning
“fraction”; therefore, in a context of numeric rafsi, you can
use any of the rafsi for “frinu” to indicate a fraction
slash.}

_{A similar convention is used for the cmavo “cu'o” of
selma'o MOI, which is closely related to “cunso”
(probability); use a rafsi for “cunso” in order to create
lujvo based on “cu'o”. The cmavo “mei” and “moi” of MOI
have their own rafsi, two each in fact: “mem”/“mei” and
“mom”/“moi” respectively.}

_{The grammar of mekso as described so far imposes a
rigid distinction between operators and operands. Some flavors
of mathematics (lambda calculus, algebra of functions) blur
this distinction, and Lojban must have a method of doing the
same. An operator can be changed into an operand with
“ni'enu'a”, which transforms the operator into a matching
selbri and then the selbri into an operand.}

_{To change an operand into an operator, we use the cmavo
“ma'o”, already introduced as a means of changing a lerfu
string such as “fy.” into an operator. In fact, “ma'o” can
be followed by any mekso operand, using the elidable terminator
“te'u” if necessary.}

_{There is a potential semantic ambiguity in “ma'o fy.
[te'u]” if “fy.” is already in use as a variable: it comes
to mean “the function whose value is always 'f”'. However,
mathematicians do not normally use the same lerfu words or
strings as both functions and variables, so this case should
not arise in practice.}