## 17.11. Mathematical uses of lerfu strings

This chapter is not about Lojban mathematics, which is explained in Chapter 18, so the mathematical uses of lerfu strings will be listed and exemplified but not explained.

• A lerfu string as mathematical variable:

Example 17.34.

 li .abu du li by. su'i cy. the-number a equals the-number b plus c
 a = b + c

• A lerfu string as function name (preceded by ma'o of selma'o MAhO):

Example 17.35.

 li .y.bu du li ma'o fy. boi xy. the-number y equals the-number the-function f of x y = f(x)

Note the boi here to separate the lerfu strings fy and xy.

• A lerfu string as selbri (followed by a cmavo of selma'o MOI):

Example 17.36.

 le vi ratcu ny.moi le'i mi ratcu the here rat is-nth-of the-set-of my rats
 This rat is my Nth rat.

• A lerfu string as utterance ordinal (followed by a cmavo of selma'o MAI):

Example 17.37.

 ny.mai
 Nthly

• A lerfu string as subscript (preceded by xi of selma'o XI):

Example 17.38.

 xy. xi ky. x sub k

• A lerfu string as quantifier (enclosed in veive'o parentheses):

Example 17.39.

 vei ny. [ve'o] lo prenu ( “n” ) persons

The parentheses are required because ny. lo prenu would be two separate sumti, ny. and lo prenu. In general, any mathematical expression other than a simple number must be in parentheses when used as a quantifier; the right parenthesis mark, the cmavo ve'o, can usually be elided.

All the examples above have exhibited single lerfu words rather than lerfu strings, in accordance with the conventions of ordinary mathematics. A longer lerfu string would still be treated as a single variable or function name: in Lojban, .abu by. cy. is not the multiplication a × b × c but is the variable abc. (Of course, a local convention could be employed that made the value of a variable like abc, with a multi-lerfu-word name, equal to the values of the variables a, b, and c multiplied together.)

There is a special rule about shift words in mathematical text: shifts within mathematical expressions do not affect lerfu words appearing outside mathematical expressions, and vice versa.