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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 ...
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Pope John Paul II was the subject of three premature obituaries.. A prematurely reported obituary is an obituary of someone who was still alive at the time of publication. . Examples include that of inventor and philanthropist Alfred Nobel, whose premature obituary condemning him as a "merchant of death" for creating military explosives may have prompted him to create the Nobel Prize; [1 ...
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 ...
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
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 ...
A proof of funds (POF) is a document such as a bank statement proving that a person or a company has the financial ability to perform a transaction or meet a potential future liability. The POF can be issued by a bank, a financial institution or a trade finance provider.
The sample probably is the substance. For example, the Kastle–Meyer test will show either that a sample is not blood or that the sample is probably blood, but may be a less common substance. Further chemical tests are needed to prove that the substance is blood.