Definition:QED

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Definition

The initials of Quod Erat Demonstrandum, which is Latin for which was to be demonstrated.

These initials were traditionally added to the end of a proof, after the last line which is supposed to contain the statement that was to be proved.


The usage is considered hopelessly old-fashioned nowadays, and is rarely seen outside nerd sitcoms.

The Halmos symbol $\blacksquare$ is usually used instead.


$\mathsf{Pr} \infty \mathsf{fWiki}$ universally uses $\blacksquare$ to signify the end of a proof.

The symbol $\Box$ is used to signify the end of a stage part way through a proof, where a subsidiary result is proved.


Also known as

Some sources render it as Q.E.D. (that is, with dots).


Internationalization

Q.E.D. is translated:

In Afrikaans: W.B.M.W.  (that is: wat bewys moes word)
In Armenian: Ի.Է.Պ.Ա.  (that is: Ինչ էլ պահանջվում եր ապացուցել)
In Bengali: অতঃ সিদ্ধ  (that is: ataha siddha)
In Bulgarian: К.Т.Д.  (that is: което трябваше да се докаже)  Pronounced:  koeto tryabvashe da se dokazhe
In Catalan: C.V.D.  (that is: com volíem demostrar)
In Czech: C.B.D.  (that is: což bylo dokázati)
In Danish: H.S.B.  (that is: hvilket skulle bevises)
In Dutch: W.T.B.W.  (that is: wat te bewijzen was)
In Esperanto: k.e.d.  (that is: kio estis demonstrenda)
In Estonian: M.O.T.T.  (that is: mida oligi tarvis tõestada)
In Finnish: M.O.T.  (that is: mikä oli todistettava)
In French: C.Q.F.D.  (that is: ce qu'il fallait démontrer)
In Georgian: რ.დ.გ.  (that is: რისი დამტკიცებაც გვინდოდა)  Pronounced:  risi damtkic'ebac' gvindoda
In German: w.z.b.w.  (that is: was zu beweisen war)
In Greek: ο.ε.δ.  (that is: ὅπερ ἔδει δεῖξαι)  Pronounced:  oper edei deixai
In Gujarati: ઇતિ સિદ્ધમ્  (that is: iti siddham)
In Hindi: इति सिद्धम्  (that is: iti siddham)
In Hebrew: מש"ל  (that is: מה שצריך להוכיח)  Pronounced:  mah shetzarich l'hochiach
In Hungarian: E.K.B.  (that is: ezt kellett bizonyítani)
In Icelandic: þ.s.s.á.  (that is: það sem sanna átti)
In Irish: R.B.T  (that is: an rud a bhí le taispéaint)
In Italian: C.V.D.  (that is: come volevasi dimostrare)
In Japanese: 結論  (that is: ketsuron)
In Kannada: ಇತಿ ಸಿದ್ಧಮ್  (that is: iti siddham)
In Latvian: k.b.j.  (that is: kas bija jāpierāda)
In Lithuanian: k.r.į.  (that is: ką ir reikėjo įrodyti)
In Marathi: इति सिद्धम्  (that is: iti siddham)
In Polish: c.b.d.u.  (that is: co było do udowodnienia)
In Portuguese: C.Q.D.  (that is: como queríamos demonstrar)
In Romanian: C.C.T.D.  (that is: ceea ce trebuia demonstrat)
In Russian: ч.т.д.  (that is: что и требовалось доказать)  Pronounced:  shto ee tryebovalos dokazat
In Sanskrit: इति सिद्धम्  (that is: iti siddham)
In Serbian: ш.т.д.  (that is: што је и требало доказати)  Pronounced:  shto ye ee trebalo dokazati
In Slovak: Č.B.T.D.  (that is: čo bolo treba dokázať)
In Spanish: Q.E.D.  (that is: queda entonces demostrado)
In Swedish: VSB  (that is: vilket skulle bevisas)
In Telugu: ఇతి సిద్ధమ్  (that is: iti siddham)
In Thai: ซ.ต.พ.  (that is: ซึ่งต้องพิสูจน์)
In Ukrainian: щ.в.д.  (that is: що і вимагалося довести)  Pronounced:  shcho ee veemagalosya dovestee
In Vietnamese: đpcm.  (that is: Điều phải chứng minh)


Technical Note

In order to render $\blacksquare$, use the template {{qed}}.

In order to render $\Box$, use the template {{qed|lemma}}.

When {{qed}} is used, it automatically adds the page on which it is implemented to Category:Proven Results.


Sources

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