Talk:Q.E.D.

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Are the squares (■, □) commonly called "tombstone notations"? If so, it should be included. --Menchi 05:36 15 Jul 2003 (UTC)

A quick google search on "tombstone notation" turns up one match, but I do like the term... ;) - Hephaestos
I do seem to recall they're called tombstones, but I don't remember exactly, so I thought it best not to mention so until I was sure :) Dysprosia 05:40 15 Jul 2003 (UTC)
Ok I checked, they're called the tombstone or halmos. In Lucida Sans Unicode (which has almost every Unicode char under the sun, it's ∎, but the Times New Roman approximations should be still appropriate Dysprosia 05:42 15 Jul 2003 (UTC) PS it turns out it renders properly :) I'll edit

Contents

[edit] ...to the ridiculous.=

"In English speaking countries the letters can also mean "Quite Easily Done" or, occasionally, "Quite Eloquently Done", or humourously "Quite Enough Done", "Quite Elegantly Done". A more colloquial translation might be "See, I Told You So".

"In Asian speaking countries, the letters sometimes mean, "Question Easy Done", in a parody of Chinglish."

  • The Hong Kong joke is a general one that I think is common among English speakers in general as "Quite Easily Done". Other stupid variations:
  • Stupid QED acronyms --

Quite Easily Done Quite Erotically Done Quite Erroneously Done Quite Esoterically Done Quite Evasivally Done

  • Is the italicized text above, from the article, actually information? --Wetman 23:54, 20 Mar 2005 (UTC)
It's information, but it's too much information. I think the existence of such backronyms is worth mentioning here, but we don't need a dozen of variations on the theme, or explanations of why they're funny. I might do some sort of rewrite at some point. EldKatt 19:33, 10 July 2005 (UTC)

[edit] Greek notation

From TFA: "This is a translation of the Greek oper edei deixai ..."

What is the Greek notation of those words? Is it ωπερ ηδηι δηιχαι?

No. One could have tried a better guess by noting that it's really hoper edei deixai with x = ks, but since Euclid is available online I've just looked it up @ http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.01.0085&query=book%3D2%3Aproposition%3D5&layout=&loc=2.5 (Be sure to configure for pre-combined diacritics; that'll probably look best.) As an added advantage, we now know where the accents should be. Shinobu 00:43, 16 July 2005 (UTC)
Should some accented characters appear as hollow squares, just copy the text to a word processor and select a font containing the right characters. Shinobu 00:50, 16 July 2005 (UTC)

[edit] asia

"In Asian countries, the letters are sometimes taken to mean (mistakenly and ungrammatically) "Question Easy Done." "

How about changing that to

"In Asian countries, the letters are sometimes taken to mean "Question Easily Done." "

? And why would this be restricted to asian countries now that it is not ungrammatical any more? --MarSch 12:33, 3 November 2005 (UTC)

I'm not sure but I think the original contributer intended to say just what he said. Correcting the grammar also changes the statement made. Effectively your're removing the original statement and inserting a new one; I'll handle both seperately:
  1. If in Asian countries Q.E.D is taken to mean "Question Easy Done" we should be able to find a source for this. Not to mention find out which Asian countries are meant (Asia is quite large, actually). I personally wouldn't mind removing this, but if someone cares enough about this to provide a source then let it stay.
  2. Q.E.D. as "Question Easily Done" seems to me to be a tongue-in-cheek interpretation. I don't think it's specifically Asian, or caused by any misunderstanding or uninformedness (is that a word?) of the real meaning.
Shinobu 22:44, 3 November 2005 (UTC)

[edit] Popular usage

I think I also remember QED being used in the Guns of Navarone, among others. Since that section is open to the addition of lots and lots of links and instances, without any objective criterium as to what to add and what not to add, is it really wise to have it? Shinobu 16:08, 13 December 2005 (UTC)

Assuming that the implied answer to the rhetorical question is no, I agree with you. Listing every instance of "popular usage" of this not uncommon phrase would not only be impossible, but also of no aid to readers. Even disregarding the practical difficulties you mention, we have to ask ourselves if anyone, ever, will want to read about it. I suspect not. EldKatt (Talk) 16:32, 13 December 2005 (UTC)

I observe the "Popular usage" section has grown since. diff Q.E.D. is a very common phrase and the "Popular usage" section will keep growing for ever, getting less and less interesting. Unless I remove it, that is. Which is exactly what I'll do. Shinobu 13:41, 7 July 2006 (UTC)

I dislike the idea of this being removed entirely, although I appreciate there is a lack of objectivity. Maybe it should spawn a Popular usage of Q.E.D. page - that way people who what to read the examples can, but those only interested in the content of this page dont have to. Remeber, just because you don't want to read about it doesn't mean no-one does. Poobarb 00:25, 8 July 2006 (UTC)

Perhaps in the see also section. Although I think trying to record every instance of popular usage is a futile and pointless endeavor, you are free to go ahead if you disagree. Yours faithfully, Shinobu 12:12, 8 July 2006 (UTC)

Being a user that apparently added one of the back-breaking entries to this section (the HBO citation), I find it a little surprising the extent of dominion over this page exerted by one user's wholesale clipping of the popular usage section. Perhaps their explanation could have at least been worded differently, on the more practical side, rather than sounding smarmy and petulant.Eudy7 07:32, 14 July 2006 (UTC)

I don't understand your complaint. In my view, the explanation was practical and clear enough, and I would appreciate a more concrete explanation of what is "smarmy and petulant" about it. Furthermore, Shinobu's suggestion of removal (as well as my agreement with it) had been on this talk page for nearly seven months without meeting any disagreement before the user actually removed the section. It could hardly have been done in a more respectful fashion. EldKatt (Talk) 12:12, 14 July 2006 (UTC)

More Concrete Explanation: I agree the history of your discussion with Shinobu largely handled the issue with pragmatism. I see the potential for excessive growth of the section, given enough time. I'm not above admitting my comment may just be sour grapes -- I find it regretful that my contribution became the catalyst for every other section contributor's work getting clipped. And my initial reaction to Shinobu's final two sentences in the comment which explained the mass edit is the source of my "smarmy and petulant" accusation. Upon another reading, I still extract a degree of flippancy in the those final two, short sentences at the close of the explanation. It's simply my interpretation, and I could be completely wrong on the question of the writer's tone or intent. Overall, the specific matter is rather insignificant in my opinion and the underlying principle doesn't rise to any level I feel needs strident debate. I simply felt a strongly worded comment was in order to remind anyone inclined to remove large amounts of material that they are removing someone's inspiration and effort, however tiny. Cheers.--Eudy7 01:02, 15 July 2006 (UTC)

[edit] Improper translations of QED/QEF?

If you look at the linked Latin lexicon (which shows the morphology), you'll notice that erat is the imprefect active indicate form of the "be" verb [see Perseus morphology as well], which corresponds exactly to the Greek ἔδει (imperfect active indicative). It is not a subjunctive or imperative form. I understand that many Mathematicians take the expression as "was to be," but I figure that is due to the fact that they are expert in Maths, not translating languages (they also often add the word "that", i.e., "that which", though the word is entirely absent from the Latin [and Greek] phrase). Is there any evidence from Latin lexicographers or grammarians, that erat can be translated as "was to be"? It seems that "was" or "was being" is the accurate translation. See 2nd conjugation ("-at" ending) 3rd person translation of the imperfect (="was") and Uses of the tenses in Latin grammar (imprefect="was").

Another related issue is that even if by some obscure convention or nuance it could be translated "was to be," that doesn't convey the ancient or current use of the expression. Where "was to be" implies "but might not have been", the whole point of appending it to some propositions and not all of them, was to point up the fact that the author thought that they had proven that proposition beyond all dispute. When QED is used today, it is used the same way — not to say the weaker "I think I've shown this," but the much stronger "I have shown this, period."

So both in terms of grammar and practice, "was to be" seems wrong. Remember, just because various Math sites say "was to be" doesn't mean it is correct — the lexicographers and grammarians must decide the issue of the proper translation of a Latin phrase. I'm open to correction on all points, however. --MonkeeSage 07:05, 7 April 2006 (UTC)

  • erat is being translated as 'was'. The 'to be' comes from converting the gerund demonstrandum into a passive infinitive. Peter Grey 07:15, 7 April 2006 (UTC)
Hmmm...that would explain the rendering. But that is odd, in that demonstrandum has a verbal root — taking it as a gerund/participal doesn't make a lot of sense to me...mabye the future could be understand as "to be (in the future)", but it reads more like "(I intended it) to be" in English, as if it had a subjunctive nuance. But, then, I'm no expert in Latin, so I won't hold out for one translation over another, I was just wondering. --MonkeeSage 09:03, 7 April 2006 (UTC)
NM, it is listed as a participle. But in this case, where demonstrandum follows the imperfect erat which takes an abstract rather than personal subject, wouldn't the rendering be "being demonstrated"? If demonstrandum is rendered as a subjunctive, then you have an assertion about a property of the quod rather than the speaker (i.e., "which was demonstrating"), where the intent seems to be with the implied subject ("which was being demonstrated [by me]", or "which [I] was demonstrating"). Ah, I don't know, I'm going to bed, it's too late to be trying to think about Latin! --MonkeeSage 09:42, 7 April 2006 (UTC)
Surely 'demonstrandum' is a gerundIVE - with the passive meaning "requiring to be demonstrated"?
Q.E.D. - that which was requiring to be demonstrated
Or if you prefer: gerundive + the verb to be = necessity. That which must be demonstrated.
That's correct - it's a gerundive, just like in Cato's famous declamation regarding Carthage. The translation is essentially correct. I think we can leave the finer details of Latin grammar to other articles. PubliusFL 12:13, 19 September 2006 (UTC)
The Greek translates quiet well to `that which it was necessary to show'. My Latin is poor (merely in progress), but I believe that `erat demonstrandum' is to be taken as a unit called a passive periphrastic construction. However, I can talk extensively about the Greek. ἔδει is the imperfect impersonal form translating roughly as 'it was necessary'. ὅπερ is an intensive form of the Greek accusative (direct object) pronoun; often in English translations of Latin and Greek, it is not improper (and sometimes necessary) to include complementizers in its translation, etc: `that which', `for which', or others. δεῖξαι is the aorist infinitive; in non-finite forms (when not a main verb), the aorist tense often denotes aspect (a quality English fails to distinguish), thus here `to show on one occasion'. It is actually difficult to communicate this well in English, but it implies that the proof is not an ongoing process, but (supposedly) has been completed and is unnecessary to consider again. No longer must this be proven to be used, its result can now be accepted without explanation in further work. It is curious, and on this point I defer to my betters in Greek, why the perfect infinite δεδεικέναι (there may be a consononental assimilation that I've missed in constructing this) is not used, since the result of this `showing' is resonant, ie lasts beyond the end of the page on which the proof culminates. Here is a page which discusses this, and then some, which I have just found while searching for the correct form of the perfect infinitive: http://www.du.edu/~etuttle/classics/nugreek/lesson9.htm ub3rm4th 19:54, 15 November 2006 (UTC)
@passive periphrastic: correct, the gerundive is commonly used for this. At school we were thought to think of the gerundive as "having to be <xyzzy>ed". Not that this is also reflected in the Latin name of this verb form. A way to remember the meaning of the gerundive: "ceterum censeo cartaginem esse delendam" - "I also think Cartago must be destroyed." Shinobu 02:23, 16 November 2006 (UTC)

[edit] Other source

I would recommend to move/rewrite/get permission/include the article QED by robin hartshorne. at the moment i add this as an external link.Marhahs 21:50, 27 September 2006 (UTC)

I expect that he won't mind its inclusion here but his email address (robin at math dot berkeley dot edu) is at the bottom of the page linked if you want to ask. He never officially published the note, nor does he intend to (I'm pretty sure). BTW, what does your first sentence mean? You want to move the article or rewrite his article or include the contents in this article or ... I'm not sure what your desire is. --Maplebed 06:33, 28 October 2006 (UTC)

[edit] Appropriate Use

As a teaching assistant / grader in mathematics, I'd like to point out that students (and journal authors) should only use "QED" appropriately -- to me, at least, it makes a very strong statement that the proof-writer is proud of their proof. There's nothing wrong with being proud, but it's annoying when QED is overused. I suggest only using it when you prove something in a very elegant fashion, or for a novel proof. In all other cases, the "tombstone" or "halmos" suffices. There are several ways to write a halmos in latex; one simple way, that works most of the time (depending on where the last line of your proof ends) is \hfill $\square$.

Of course, this is only my opinion, but I suspect others might agree. Agree, disagree? Lavaka 17:53, 14 February 2007 (UTC)

[edit] Foreign equivalents

Okay, I deserve the blame for this since I started it with "qcfd", but the proliferation of foreign equivalents of "qed" is getting ridiculous. I can defend "qcfd" in that French is a major mathematical language, but without disrespect to the Finnish I can say that only they will ever see "mot". I don't want to draw the line arbitrarily, but maybe the foreign translations can be reduced to just the French, German, and Russian (the canonical three other mathematical languages) and a note that other equivalents can be found in the language-specific wikipedias in the sidebar. Ryan Reich 02:28, 7 March 2007 (UTC)

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