Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

U

335 U ultrafilter The Latin preposition ultra means beyond. The noun filter is from the medieval Latin filtrum, which means felt. See the entry filter. An ultrafilter for a set X is a filter for X such that for each A X, either A  or X – A  but not both. umbilical Umbilīcus is the Latin word for the navel; it is related to the Greek noun of the same meaning ÑmfalÒj. The Latin adjective umbilicaris, with the meaning pertaining to the navel, was formed by adding the adjectival suffix -aris to the stem of the noun; in medieval times there arose the additional adjective umbilicalis with the same meaning. An umbilical point of a surface is a point P on that is either a circular point or a planar point of ; in the former case, the surface near P resembles a sphere, and in the latter case it resembles a plane there. See James and James. umbra This is the Latin word for shade or shadow. unconditional The prefix un- is the Germanic equivalent of the Greek alpha privativum ¢- and the Latin in-; it negates the adjective to which it is adjoined. It should not be added to words of Latin origin, for which the prefix in- is appropriate. An unconditional or absolute inequality is an inequality that is true for all values of the variable, for example, x4 + 1 > x. See the entry conditional. undecidable See the entry decidable. Undecidable propositions are propositions that cannot be proven true or false. undecillion This is an absurd word supposed to mean 106 + 11(3) . It is less comical to say “ten to the thirty-ninth.” Undecem is the Latin word for eleven; -illion is derived from the Latin mille, a thousand, with the augment -on (originally -one in Italian), which means big. A million is just a big thousand. ‫ڕ‬ ‫ڕ‬ ‫ڕ‬ ‫ڦ‬ ‫ڦ‬ ‫ڦ‬ 336 undefined The Germanic negative prefix un- has been added to the word defined of Latin origin to produce the hybrid undefined. It would have been better to say indefined as we say indefinite, but it is too late now. Defined is from the verb definio, definire, definivi, definitus, which means to set the boundaries. The plural noun fines in Latin means enclosed area, territory. The force of the prefix de- is to add the sense of thoroughness to the action. undetermined The Germanic negative prefix un- has been added to the word determined of Latin origin to produce the hybrid undetermined. Indetermined would have been the correct formation, in the same way as we say indeterminate. Determined is derived from the Latin verb determino, determinare, determinavi, determinatus, which means to set the boundaries. The noun terminus in Latin means the boundary mark. In the theory of differential equations, the method of undetermined coefficients is a method of determining a particular solution of a linear non-homogeneous differential equation. One guesses that the solution must be of a certain form with certain parameters and then proceeds to determine the parameters. The force of the prefix de- is to give the sense of thoroughness to the action. uni- This Latin prefix is derived from the adjective unus, which means one. It is added to other adjectives of Latin origin to give the meaning of sole, unique. It cannot be added to adjectives derived from other languages without producing a low word. The Greek equivalent is mono-, mono-. unicursal This nineteenth-century adjective is the combination of the Latin particle uni- and the medieval Latin adjective cursalis. (The proper form of the adjective is the ancient cursualis.) The Latin verb curro, currere, cucurri, cursus means to run. From its fourth principal part is derived the noun cursus, cursūs, running. The adjective unicursal is applied to paths in space and is a synonym for continuous; the idea is that the path can be drawn with one course of the pen. uniform The Latin adjective uniformis means having one form, simple. 337 uniformity The Latin noun uniformitas, simplicity, came into French as uniformité , which then became the English uniformity. unilateral The Romans added the prefix uni- to an adjective to express the restriction only or one. The formation unilateralis is a modern word meaning pertaining to one side (latus), but it is well made on the ancient model. unimodal This is a modern word used in the theory of probability. A unimodal random variable is one that has one and only...