The words QED (Latin for " what was to be proved " ) traditionally include a logical or mathematical proof from, often in the abbreviated form q. e d
In a statement that has yet to be proved are the words quod eat demonstrandum or " what has to be proved ."
The Latin words are a translation of the Greek ὅπερ ἔδει δεῖξαι, graduating with the mathematicians of ancient Greece their evidence, including Euclid and Archimedes.
For the purpose of visual clarity, the uppercase Q. E. D. as after the Latin capitalis monumentalis is often the case, especially in English.
Jokingly q. e d in a false proof as quo errat demonstrator (in which the evidence is wrong end ) or quod est dubitandum (which is doubtful ) read.
Alternative symbol ■
Nowadays, instead of q. e d also often symbolized by a black square ■. It is called grave, crate or according to Erstverwenders Halmos. Sometimes the grave stone is also shown open: □
■ can be jokingly read as square demon - stratum. Some authors use ■ but rather q only for short proofs, with long and complicated proofs. e d
Unicode provides the End of Proof character U 220 E ( ∎ ), but also U 25 A0 ( ■, black square ) and U 2023 ( ‣, triangular point) as alternative options.