How to say "lower bound" and "upper bound"?

Question

Lower bound, upper bound, infimum, supremum, minimum, and maximum are concepts in mathematics. I cannot find translations of them in Wikipedia and Latin dictionaries. Here are their translations in other Romance Languages:

En. | Lower Bound | Upper bound | Infimum          | Supremum        | Minimum | Maximum
Fr. | Majorant    | Minorant    | Infimum          | Supremum        | Minimum | Maximum
Es. | Mayorante   | Minorante   | Infimo           | Supremo         | Minimo  | Maximo
It. | Maggiorante | Minorante   | EstremoInferiore | EstremoSuperiore| Minimo  | Massimo

so it seems like that Infimum, Supremum, Minimum, Maximum are plausible translations in Latin, but I am not sure about Lower bound and Upper bound. Wiktionary suggests they are the present participle of verbs evolved from the Latin root words Major and Minor via an intermediate step (majoro, -are, -avi, -atum?).

Are Majorans, -tis and Minorans, -tis the closest translations of lower and upper bounds in Latin?

Answer 1

The words majorans (or maiorans) and minorans are present participles of the verbs maiorare and minorare. I have not found maiorare, but minorare does exist. However, the meaning is not exactly what would hope.

It is important to notice that the terms you are after are technical terms, and it would be too much to assume that they come from classical Latin words with exactly the right tone. Mathematical analysis as we know it did not exist in ancient Rome. (There were some precursors at the time, but I would argue that actual analysis had to wait for over a millennium.)

Deriving the verb maiorare from maior makes sense by analogy to minor > minorare and other first conjugation derivatives. The meanings aren't precisely what you might expect, but they make good technical terms: the analogy to other languages is clear, and the meanings are closely related to the underlying words maior and minor. If one reads maiorare/minorare as "to be bigger/smaller", which is not entirely unreasonable, then the meanings are precisely the ones you are after.

As a mathematician, I can promise that clarity and similarity to other languages is crucial if you ever want to successfully introduce new Latin words into mathematical literature. The proposed maiorans and minorans look very good in this respect, and I wholly support choosing them as the translations for "majorant" / "upper bound" and "minorant" / "lower bound". I would be happy to use these terms if I ever end up writing about related topics in Latin. (I have published a little something about mathematics in Latin.)

As a side note, let me add one pair to your sextuplet: limes superior and limes inferior. They are sometimes called with these Latin names in English, and these are perfectly valid Latin expressions. In Italian they are limite superiore/inferiore, in French limite supérieure/inférieure, and in Spanish límite superior/inferior. The most common English versions I hear are the "lim sup" and "lim inf".