## 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 |

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 |

**Example 18.63.
**

re | pi | ze | re | ji'i | ma'u |

two | point | seven | two | approximation | positive-sign |

**Example 18.64.
**

re | pi | ze | pa | ji'i | ni'u |

two | point | seven | one | approximation | negative-sign |

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 18.1, 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 18.1. Descriptions in general are outside the scope of this chapter.