## 18.9. Approximation and inexact numbers

The following cmavo are discussed in this section:

 ji'i PA approximately su'e PA at most su'o PA at least me'i PA less than za'u PA more than

The cmavo ji'i (of selma'o PA) is used in several ways to indicate approximate or rounded numbers. If it appears at the beginning of a number, the whole number is approximate:

Example 18.60.

 ji'i vo no approximation four zero
 approximately 40

If ji'i appears in the middle of a number, all the digits following it are approximate:

Example 18.61.

 vo no ji'i mu no four zero approximation five zero
 roughly 4050 (where the “four thousand” is exact, but the “fifty” is approximate)

If ji'i appears at the end of a number, it indicates that the number has been rounded. In addition, it can then be followed by a sign cmavo (ma'u or ni'u), which indicate truncation towards positive or negative infinity respectively.

Example 18.62.

 re pi ze re ji'i two point seven two approximation
 2.72 (rounded)

Example 18.63.

 re pi ze re ji'i ma'u two point seven two approximation positive-sign
 2.72 (rounded up)

Example 18.64.

 re pi ze pa ji'i ni'u two point seven one approximation negative-sign
 2.71 (rounded down)

Example 18.62 through Example 18.64 are all approximations to te'o (exponential e). ji'i can also appear by itself, in which case it means approximately the typical value in this context.

The four cmavo su'e, su'o, me'i, and za'u, also of selma'o PA, express inexact numbers with upper or lower bounds:

Example 18.65.

 mi catlu su'e re prenu I look-at at-most two persons

Example 18.66.

 mi catlu su'o re prenu I look-at at-least two persons

Example 18.67.

 mi catlu me'i re prenu I look-at less-than two persons

Example 18.68.

 mi catlu za'u re prenu I look-at more-than two persons

Each of these is a subtly different claim: Example 18.66 is true of two or any greater number, whereas Example 18.68 requires three persons or more. Likewise, Example 18.65 refers to zero, one, or two; Example 18.67 to zero or one. (Of course, when the context allows numbers other than non-negative integers, me'i re can be any number less than 2, and likewise with the other cases.) The exact quantifier, exactly 2, neither more nor less is just re. Note that su'ore is the exact Lojban equivalent of English plurals.

If no number follows one of these cmavo, pa is understood: therefore,

Example 18.69.

 mi catlu su'o prenu I look-at at-least-[one] person

is a meaningful claim.

Like the numbers in Section 18.8, all of these cmavo may be preceded by pi to make the corresponding quantifiers for part of a whole. For example, pisu'o means at least some part of. The quantifiers ro, su'o, piro, and pisu'o are particularly important in Lojban, as they are implicitly used in the descriptions introduced by the cmavo of selma'o LA and LE, as explained in Section 6.7. Descriptions in general are outside the scope of this chapter.