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Encyclopedia > Q.E.D
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.

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 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".



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