Monomial

Part of speech: noun

Definitions

1. A mathematical expression formed by a product of numbers and variables, where the variables have non-negative integer exponents and no addition or subtraction exists
2. An expression representing a single term made up of real numbers and variables, combined through multiplication, with each variable raised to a non-negative whole number
3. A single mathematical term that consists of a product of constants and variables, with the variables having non-negative integral powers and lacking any additive components

Etymology: "Monomial" is a formation built from Greek parts: "mono-" meaning "one" and a second element ending in "-nomial," which comes from "nomos" (a division or part) with the same sense of counting terms that "binomial" and "polynomial" use. Together they name an algebraic expression made of a single term, such as 3x² or -7ab. The word was first formed as "mononomial," with a repeated "-nono-" sound in the middle that looks like a doubled prefix. Speakers and writers dropped one of the "no" syllables through haplology, the common process by which a repeated sound sequence is shortened, leaving the streamlined "monomial" we use now. The result sits in a family with "binomial" (two terms) and "polynomial" (many terms), so the number prefix tells you immediately how many parts an expression contains.

Synonyms: single term, univariate, one-term expression, factor, variable

Antonyms: polynomial, multinomial, binomial, compound, combined