Chapter 18: lojbau mekso: Mathematical Expressions in Lojban
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:
However, many combinations are as yet undefined:
✥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.