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Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. Help. Pages in category "Lists of apologies" The following 4 pages are in this ...
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 Mathematician's Apology 1st edition Author G. H. Hardy Subjects Philosophy of mathematics, mathematical beauty Publisher Cambridge University Press Publication date 1940 OCLC 488849413 A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal justification ...
Indeed, the above proof that the law of excluded middle implies proof by contradiction can be repurposed to show that a decidable proposition is ¬¬-stable. A typical example of a decidable proposition is a statement that can be checked by direct computation, such as " n {\displaystyle n} is prime" or " a {\displaystyle a} divides b ...
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
a sentence justified by the citation of (1) a rule of inference and (2) the prior line or lines of the proof that license that rule. Introducing a new assumption increases the level of indentation, and begins a new vertical "scope" bar that continues to indent subsequent lines until the assumption is discharged.
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