# Definition:Lemma

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## Definition

A **lemma** is a statement which is proven during the course of reaching the proof of a theorem.

Logically there is no qualitative difference between a **lemma** and a theorem.

They are both statements whose value is either true or false.

However, a **lemma** is seen more as a stepping-stone than a theorem in itself (and frequently takes a lot more work to prove than the theorem to which it leads).

Some lemmas are famous enough to be named after the mathematician who proved them (for example: Abel's Lemma and Urysohn's Lemma), but they are still categorised as second-class citizens in the aristocracy of mathematics.

## Also see

## Linguistic Note

The plural of **lemma** is either **lemmas** or **lemmata**.

## Sources

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 1$: Some mathematical language: Axiom systems - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**lemma** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**lemma** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**lemma** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**lemma**