proof by contradiction
1proof by contradiction — noun Proof of a statement adduced by deriving a contradiction from the statements negation. Syn: reductio ad absurdum …
2Contradiction — In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other.… …
3Proof of Bertrand's postulate — In mathematics, Bertrand s postulate (actually a theorem) states that for each n ≥ 2 there is a prime p such that n < p < 2 n . It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan. The gist of …
4Proof that e is irrational — In mathematics, the series representation of Euler s number e : e = sum {n = 0}^{infty} frac{1}{n!}!can be used to prove that e is irrational. Of the many representations of e, this is the Taylor series for the exponential function e y evaluated… …
5Proof that the sum of the reciprocals of the primes diverges — In the third century BC, Euclid proved the existence of infinitely many prime numbers. In the 18th century, Leonhard Euler proved a stronger statement: the sum of the reciprocals of all prime numbers diverges. Here, we present a number of proofs… …
6Proof by assertion — is a logical fallacy in which a proposition is repeatedly restated regardless of contradiction. Sometimes this may be repeated until challenges dry up, at which point it is asserted as fact due to its not being contradicted (argumentum ad… …
7Proof of impossibility — A proof of impossibility, sometimes called a negative proof or negative result , is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or… …
8Proof complexity — In computer science, proof complexity is a measure of efficiency of automated theorem proving methods that is based on the size of the proofs they produce. The methods for proving contradiction in propositional logic are the most analyzed. The… …
9Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… …
10Proof that π is irrational — Although the mathematical constant known as pi; (pi) has been studied since ancient times, and so has the concept of irrational number, it was not until the 18th century that π was proved to be irrational.In the 20th century, proofs were found… …
