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In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or " ") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "quod erat demonstrandum". It is inspired by the typographic practice of end marks, an element that marks the end of an article. [1] [2]
The beginning of a proof usually follows immediately thereafter, and is indicated by the word "proof" in boldface or italics. On the other hand, several symbolic conventions exist to indicate the end of a proof. While some authors still use the classical abbreviation, Q.E.D., it is relatively uncommon in modern mathematical texts.
Used along with block elements are box-drawing characters, shade characters, and terminal graphic characters. These can be used for filling regions of the screen and portraying drop shadows. Its block name in Unicode 1.0 was Blocks. [3]
In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...
A proof of an etching by Hubert von Herkomer, without text, which would appear in the empty rectangular portion of the page above the artist's signature.. The term "proof" is generally, but not consistently, applied only to prints from the late eighteenth-century onwards, beginning with the English mezzotinters, who began the practice of issuing small editions of proofs for collectors, often ...
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Proof sheets were the means by which syndicates provided newspapers with black-and-white line art for the reproduction of strips (which they arranged to have colored in the case of Sunday strips). Michigan State University Comic Art Collection librarian Randy Scott describes these as "large sheets of paper on which newspaper comics have ...
For example, when α is the ground plane and β is the horizon plane, then the vanishing line of α is the horizon line β ∩ π. To put it simply, the vanishing line of some plane, say α , is obtained by the intersection of the image plane with another plane, say β , parallel to the plane of interest ( α ), passing through the camera center.