## 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
 xₖ

• 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.