## Chapter 17: As Easy As A-B-C? The Lojban Letteral System And Its Uses

### 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:

✥11.1 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):

✥11.2 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):

✥11.3 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):

✥11.4 ny.mai Nthly

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

✥11.5 xy. xi ky. x sub k

A lerfu string as quantifier (enclosed in “vei … ve'o” parentheses):

✥11.6 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 x b x c” but is the variable “abc”. (Of course, a local convention could exist 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.