0
$\begingroup$

How exactly does a lemma differ from another type of proposition (like a theorem or corollary)?

I think it is that lemmas are used to help prove theorems and coroallary are specific cases of theorems. Is this correct?

$\endgroup$
5
$\begingroup$

There is no formal difference between a "theorem" and "lemma".

As you have noticed, propositions tend to be called "lemmas" when the author's main purpose in proving them is as a stepping stone to proving something more interesting. But ultimately is is subjective what one considers "interesting" enough to be called a theorem.

There are also results that are important enough to have capitalized names and nevertheless are called lemmas, such as for example Zorn's lemma. This is sometimes a pure accident of history, but also sometimes to suggest that whereas the result does not look particularly interesting on its surface, it is a useful component for proving more substantial propositions.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.