Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
So far our examples have been isolated mekso (it is legal to have a bare mekso as a sentence in Lojban) and equation bridi involving “du”. What about inequalities such as “x < 5”? The answer is to use a bridi with an appropriate selbri, thus:
✥7.1 li xy. mleca li mu the-number x is-less-than the-number 5
Here is a partial list of selbri useful in mathematical bridi:
du x1 is identical to x2, x3, x4, ... dunli x1 is equal/congruent to x2 in/on property/quality/dimension/quantity x3 mleca x1 is less than x2 zmadu x1 is greater than x2 dubjavme'a x1 is less than or equal to x2 [du ja mleca, equal or less] dubjavmau x1 is greater than or equal to x2 [du ja zmadu, equal or greater] tamdu'i x1 is similar to x2 [tarmi dunli, shape-equal] turdu'i x1 is isomorphic to x2 [stura dunli, structure-equal] cmima x1 is a member of set x2 gripau x1 is a subset of set x2 [girzu pagbu, set-part] na'ujbi x1 is approximately equal to [namcu jibni, number-near] terci'e x1 is a component with function x2 of system x3
Note the difference between “dunli” and “du”; “dunli” has a third place that specifies the kind of equality that is meant. “du” refers to actual identity, and can have any number of places:
✥7.2 py. du xy.boi zy. “p” is-identical-to “x” “z” p = x = z
Lojban bridi can have only one predicate, so the “du” is not repeated.
Any of these selbri may usefully be prefixed with “na”, the contradictory negation cmavo, to indicate that the relation is false:
✥7.3 li re su'i re na du li mu the-number 2 + 2 is-not equal-to the-number 5. 2 + 2 ½ 5
As usual in Lojban, negated bridi say what is false, and do not say anything about what might be true.