lemmata

A mathematician writes several lemmata on a whiteboard.

Definition

1. Noun (plural of ):
   • In mathematics: "lemmata" refers to a set of auxiliary propositions or theorems used to prove a larger theorem. A lemma is a minor or intermediate result, often serving as a stepping stone.
   • In linguistics: "lemmata" are the base or canonical forms of words (e.g., the singular form of a noun or the infinitive form of a verb) under which related inflected forms are grouped in dictionaries or lexicons. For example, "run" is a lemma that includes "runs," "ran," and "running."
   • In publishing: "lemmata" can also refer to the headings or annotations added to illustrations, such as explanatory captions or marginal notes.

Usage Examples

• Mathematics:
  • The proof relies on several lemmata that were established earlier in the chapter. (Auxiliary propositions used to demonstrate a main theorem.)
• Linguistics:
  • The dictionary lists all inflected forms under their respective lemmata. (Base forms of words in a lexicon.)
• Publishing:
  • The lemmata beneath the diagrams explained the complex machinery. (Captions or annotations for images.)

Advanced Usage

• "to establish a lemma": to prove a small, subsidiary proposition.
  • Before proving the main theorem, the mathematician established two crucial lemmata. (Proved intermediate results.)
• "lemma in a corpus": in computational linguistics, a lemma is the canonical form used to group word variants.
  • The software extracted all lemmata from the text to analyze vocabulary frequency. (Base word forms from a body of text.)

Variants and Related Words

• Lemma (n, singular): one of the lemmata.
  • This lemma is essential for the proof. (A single auxiliary proposition.)
• Lemmatization (n): the process of grouping inflected forms under their lemma.
  • Lemmatization helps in natural language processing tasks. (Linguistic analysis technique.)
• Lemmatize (v): to reduce a word to its lemma.
  • The algorithm can lemmatize verbs automatically. (Convert to base form.)

Synonyms

• Subtheorem: a minor theorem used in proving a larger one.
• Canonical form: the standard or base form of a word.
• Caption: a heading or explanatory note for an image.

Related Idioms

• "Lemma and corollary": used metaphorically to describe a main point and its direct consequence.
  • His argument was like a lemma and corollary—first the premise, then the logical result. (A primary statement and its follow-up.)
• "To prove a lemma": to establish a small but necessary truth.
  • Before solving the case, the detective had to prove several lemmata about the timeline. (Establish intermediate facts.)

Note on Usage

The word "lemmata" is the formal Latin plural of "lemma." In modern English, the plural "lemmas" is more common in informal contexts, but "lemmata" remains standard in academic writing, especially in mathematics and linguistics.