lemma

lemma — noun

1. the simplest grammatical version of a word chosen as the main heading in a dicti

1.nounB2
Definition

the simplest grammatical version of a word chosen as the main heading in a dictionary, representing all its other forms such as the past tense or the plural

Example

The dictionary entry for the lemma 'run' covers more than fifty different meanings.

lemma as dictionary headword covering all related forms

In an English dictionary, the lemma 'go' stands for forms like 'goes', 'went', and 'going'.

Common collocations
  • dictionary lemma
  • lemma entry
  • base lemma
  • lemma form
Synonyms
  • headword

    the word placed at the start of a dictionary entry; 'lemma' is more common in academic linguistics

  • citation form

    the grammatical base form used to represent all variants; interchangeable with 'lemma' in morphology

  • entry word

    informal term for the word being defined in a dictionary; less technical than 'lemma'

Grammar Patterns

the lemma [word]

lemma of [word]

Usage Note

The lemma is always the uninflected base form of a word. This sense is the standard one in lexicography and corpus linguistics.

Common Mistakes

The lemma "runs" appears in the dictionary.
The lemma "run" appears in the dictionary.
The lemma is always the base form, not an inflected form.

2. a statement in mathematics or logic that is proved to be true and then used as a

2.nounC1
Definition

a statement in mathematics or logic that is proved to be true and then used as a stepping stone in proving a larger or more important theorem

Example

The mathematician proved a lemma about prime numbers before moving on to the main theorem.

lemma as proof step toward a theorem

Vikram used a well-known lemma to check the logic in his geometry assignment.

Common collocations
  • prove a lemma
  • state a lemma
  • lemma about
  • supporting lemma
  • technical lemma
Synonyms
  • proposition

    any statement that can be true or false; a lemma is a specific type of proposition used as a proof step

  • theorem

    a major result that is the goal of a proof; a lemma is usually a smaller helper step toward a theorem

  • axiom

    a statement accepted as true without requiring proof; a lemma must be proved

  • corollary

    a result that follows directly from a proved theorem; a lemma leads toward a theorem rather than following from it

Grammar Patterns

lemma + about + noun phrase

lemma + in + noun phrase

prove a lemma

lemma + that-clause

Usage Note

Distinguish from 'theorem' (a major result that the proof aims to establish) and 'axiom' (a starting assumption taken as true without proof). A lemma is typically a helper result that is proved and then reused.

Common Mistakes

The scientist proved a lemma before collecting data from the experiment.
The mathematician proved a lemma before tackling the main theorem.
Lemma is a logical or mathematical concept, not used in empirical scientific experiments.

3. the main theme, argument, or subject that a written work explores, sometimes ind

3.nounC1
Definition

the main theme, argument, or subject that a written work explores, sometimes indicated by a heading or title at the start

Example

The lemma of the essay was stated clearly in the opening paragraph.

lemma as stated theme of a written work

Mira could not follow the article because its lemma was confusing and poorly explained.

Common collocations
  • lemma of the work
  • stated lemma
  • underlying lemma
Synonyms
  • theme

    the central idea of a work; 'lemma' is a more formal term, often appearing as a heading

  • subject

    the topic being discussed; 'lemma' is specific to the opening statement of the topic

Grammar Patterns

the lemma of + noun phrase

Usage Note

Archaic or formal register. This sense is common in literary criticism and manuscript studies. Distinguish from sense 1 (DICTIONARY HEADWORD): sense 3 refers to the theme or subject itself, not to a word's base dictionary form.

Word family

  • lemmatize
    verbC2
  • lemmatization
    nounC2

Synonym discussion

Sense: noun/2

In mathematics and logic, lemma, proposition, theorem, axiom, and corollary all refer to statements within a proof system, but each plays a different role. A proposition is the most general term — any statement that can be true or false. An axiom is a starting assumption accepted without proof. A lemma is a helper statement that is proved and then reused to prove something bigger. A theorem is the main result the proof works toward. A corollary follows directly from a theorem as an immediate consequence. For example: starting from an axiom about equality, a mathematician may prove a lemma about triangle congruence, use it to prove the Pythagorean theorem, and then note as a corollary that a triangle with sides 3-4-5 is right-angled.

proposition ↗theorem ↗axiom ↗corollary

Common collocations

Nouns

Phrases

  • prove a lemma
  • state a lemma

Prepositions

Etymology

GreekLatinEnglish

The word 'lemma' traces back to the Greek 'lēmma' (λῆμμα), meaning 'something taken or received, an assumption, a premise.' This came from the verb 'lambanein,' meaning 'to take, receive, or seize.' The term passed into Latin as 'lemma' with the sense of a proposition taken for granted, and entered English in the late 1500s. The dictionary-entry meaning developed later, in the context of modern linguistics and lexicography.