18.21. 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:

Example 18.139.

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:

Example 18.140.

li	ci	na'e	su'i	vo	du	li	pare
The-number	3	non-	plus	4	equals	the-number	12.

Example 18.141.

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:

Example 18.142.

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:

Example 18.143.

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:

Example 18.144.

la	zemei	poi	gunta
Those-named-the	Sevensome	who	attack

la	tebes.	pu	nanmu
that-named	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.