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lojbau mekso: Mathematical Expressions in Lojban
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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 x3Note 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.
Previous
Forethought operators (Polish notation, functions) |
lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
Next
Indefinite numbers |