Talk:Lemma (mathematics)

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Term also used in linguistics[edit]

the term lemma is apparently also used in linguistics (meaning a word item in the mental lexicon?) (80.109.255.5 17:40, 16 Apr 2005 (UTC))

Etymology[edit]

I think the Greek word you are referring to is "λείμμα". minatsu

Could you tell us why you believe so? Both λεμμα and λείμμα exist. -- Jitse Niesen (talk) 13:43, 12 December 2005 (UTC)[reply]

I guess we were both wrong. I did a little bit of research and found out that the correct word is "λήμμα" (which you already have fixed). Yet I have to verify the original root of the word with some of my scholar friends. I can assure you that the current word used in Greek is "λήμμα" (which I guess you already know). Nevertheless here is a good search tool for you to use in the future for Greek words:

http://www.in.gr/dictionary/lookup.asp?Word=%EB%DE%EC%EC%E1&TranslateButton2=%CC%E5%F4%DC%F6%F1%E1%F3%E7

Regards

minatsu

Another source says Greek "lemma" means shell. I recall having heard it means horn (as in dilemma: two horns). Does it really mean gift/bribe? --LA2 16:47, 22 August 2006 (UTC)[reply]

Lemma vs. theorem[edit]

"There is no inherent distinction between a lemma and a theorem."

That's true in a formal sense, but in practice the two terms are used with significantly different semantics. One is rarely in doubt about which label to apply to a new result. Thoughts? Arvindn 01:39, 5 April 2006 (UTC)[reply]

Current wording is good: "no formal distinction" clarifies that the formal content of the word is identical, though the semantic use of the word is distinctive.--165.196.163.22 (talk) 19:02, 1 December 2009 (UTC)[reply]

My suggestion: People who just want to use a theory should need to look only at its theorems (and corollaries), while developpers of the theory will need to look also at its lemmas. An analogy could be made to the area of software engineering: a proposition is labelled "theorem" in order to put it in the "export interface" of the theory, while an auxiliary proposition to be hidden is labelled "lemma". Of course, labelling is largely a subjective decision, but there are criteria for good interfaces (simplicity, generality, etc.). A famous proposition called "lemma" would then be a result of an interface design flaw. Jochen Burghardt (talk) 18:52, 22 May 2013 (UTC)[reply]

Uh, utter nonsense? Why do you have to over-complicate things, Jochen? Just take things for what they are. Lemmas and theorems have nothing to do with concealing anything. The analogy is wrong. The difference between lemmas and theorems is relational and conventional/axiological: a lemma is a theorem which is used to prove another theorem. In deductive sciences, one begins with principles or axioms and through syllogistic reasoning, derives all of the consequences which are entailed by those axioms. All propositions derived form axioms are theorems. One theorem is another's lemma, though the mathematical language applies a nomenclature that generally tends to call only some things lemmas and others theorems by convention, or, because the word "theorem" is used when referring to more important or valuable theorems while lemmas are seen as less theorems which support more important theorems. A better analogy would be that between genus and species. Truly, the distinction is relative: if A is a species of B and B is a species of C, then C is the genus of A. — Preceding unsigned comment added by 24.34.227.5 (talk) 14:04, 4 August 2014 (UTC)[reply]

Couchman's lemma[edit]

I can't find this by Google. Now, there are loads of things I can't find by Google, but not if it is "one of the most powerful mathematical results" as claimed. So, I'm calling shenanigans. Feel free to add back with link. --174.119.186.126 (talk) 00:42, 25 October 2010 (UTC)[reply]

Consider the source of the contribution. The edit was made on August 24, 2009, from the IP address 210.84.58.243. There were four contributions made from this address, all on the same date. Two were to the Tom Bosley article, where the contribution was "Tom Bosley likes all the sausage.", later amended to "Tom Bosley gets all the sausage." The third was to the Modular Arithmetic article, and was "All your congruence are belong to us." The final contribution was the "Couchman's lemma" sentence in this article. While it's entirely possible for someone to make a genuine contribution to an article in addition to trolling/vandalizing Wikipedia in other articles, it's highly unlikely.--Chuckhoffmann (talk) 11:22, 30 October 2013 (UTC)[reply]

Gauss's lemma[edit]

Which of Gauss's lemmas is intended? The link leads to a disambiguation page. 202.36.179.68 (talk) 01:09, 22 July 2011 (UTC)[reply]

Bold lemma[edit]

Removed the bold format in the list of lemmas. I could find no explanation for why some were bold and others were not. If you want to restore the bold formatting please explain what it means, clearly and prominently. Thanks Nick Beeson (talk) 23:13, 26 April 2023 (UTC)[reply]