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lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
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The following cmavo are discussed in this section:
ci'i PA infinity
ka'o PA imaginary i, sqrt(-1)
pai PA pi (approx 3.14159...)
te'o PA exponential e (approx 2.71828...)
fi'u PA golden ratio, phi,
(1 + sqrt(5))/2 (approx. 1.61803...)
The last cmavo is the same as the fraction sign cmavo: a
fraction sign with neither numerator nor denominator represents
the golden ratio.
Numbers can have any of these digit, punctuation, and special-number cmavo of Sections 2, 3, and 4 in any combination:
4.1) ma'u ci'i
+¥
4.2) ci ka'o re
3i2 (a complex number equivalent to ``3 + 2i'')
Note that ``ka'o'' is both a special number (meaning ``i'') and
a number punctuation mark (separating the real and the
imaginary parts of a complex number).
4.3) ci'i no
infinity zero
À
0 (a transfinite cardinal)
The special numbers ``pai'' and ``te'o'' are mathematically important, which is why they are given their own cmavo:
4.4) pai
pi
4.5) te'o
e
However, many combinations are as yet undefined:
4.6) pa pi re pi ci
1.2.3
4.7) pa ni'u re
1 negative-sign 2
Example 4.5 is not ``1 minus 2'', which is
represented by a different cmavo sequence altogether. It is a
single number which has not been assigned a meaning. There are
many such numbers which have no well-defined meaning; they may
be used for experimental purposes or for future expansion of
the Lojban number system.
It is possible, of course, that some of these ``oddities'' do have a meaningful use in some restricted area of mathematics. A mathematician appropriating these structures for specialized use needs to consider whether some other branch of mathematics would use the structure differently.
More information on numbers may be found in Sections 8 to 12.
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Previous
Signs and numerical punctuation |
lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
Next
Simple infix expressions and equations |