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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 inlcuding
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.
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 (//) or three dots in a triangle.
Unicode provides the "End of Proof" character U+220E (∎), but also provides U+25A0 (■, black square) and U+2023 (‣, triangular bullet) as alternates.
In
Hong Kong, students jokingly reinterpret ''Q.E.D.'' as ''"Question Easy Done"'' (in
Chinglish) after they finish a "difficult" mathematical proof in their schoolwork. Similarly, in English speaking countries the letters can also mean ''"Quite Easily Done"'' or, occasionally, ''"Quite Eloquently Done"''.
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