Q.E.D.
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- For other meanings of the abbreviation "QED", see QED.
Q. E. D. is an abbreviation of the Latin phrase "quod erat demonstrandum" (literally, "that which was to be demonstrated"). This is a translation of the Greek oper edei deixai which was used by many early mathematicians including Euclid and Archimedes. Q.E.D. may be written at the end of mathematical proofs to show that the result required for the proof to be complete has been obtained. It is not seen as frequently now as in earlier centuries.
Modern-day Usage
End-of-proof symbolism in the present day is often the symbol ■ (solid black square) called the tombstone or halmos (after Paul Halmos who pioneered its use). The tombstone is sometimes open; □ (hollow black square). Another simple way of stating that the proof is complete is to simply write "proven" or "shown" in parentheses after the final step of the proof, or to draw two forward slashes (//).
Unicode provides the "End of Proof" character U+220E (∎), but also provides U+25A0 (■, black square) and U+2023 (‣, triangular bullet) as alternates.
Variations of acronym
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".
In Asian speaking countries, the letters sometimes mean, "Question Easy Done", in a parody of Chinglish.
There exists another Latin phrase, with a slight difference in meaning, but a similar, if less common usage. Quod erat faciendum translates into English as "Which was to be done." This is usually shortened to QEF
Incidentally, some people prefer to use the more tongue-in-cheek WWWWW or <math>W^5<math> which stands for the English, "Which Was What Was Wanted."
Other Q.E.D.'s
Q.E.D. was the title of a short-lived adventure series starring Sam Waterston as Professor Quentin Everett Deverill (the title character). Set in Edwardian England, the Professor was a sort of Sherlock Holmes-like character, with a smattering of what was soon to be known as steampunk.ca:Q.E.D. da:Latin:Q de:Quod erat demonstrandum es:Q.E.D. fr:CQFD hu:Quod erat demonstrandum it:Quod erat demonstrandum ja:Q.E.D. nl:Q.E.D. ru:Q.E.D. sv:Q.E.D. zh:Q.E.D.