Search results
Results from the WOW.Com Content Network
Cayley's formula; Cayley's theorem; Clique problem (to do) Compactness theorem (very compact proof) Erdős–Ko–Rado theorem; Euler's formula; Euler's four-square identity; Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel ...
In 1847, Gabriel Lamé outlined a proof of Fermat's Last Theorem based on factoring the equation x p + y p = z p in complex numbers, specifically the cyclotomic field based on the roots of the number 1. His proof failed, however, because it assumed incorrectly that such complex numbers can be factored uniquely into primes
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Sir Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove using previous ...
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
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 ...
This is perhaps the simplest known proof, requiring the least mathematical background. It is an attractive example of a combinatorial proof (a proof that involves counting a collection of objects in two different ways). The proof given here is an adaptation of Golomb's proof. [1] To keep things simple, let us assume that a is a positive integer.
Kirby–Paris theorem (proof theory) Kirchberger's theorem (discrete geometry) Kirchhoff's theorem (graph theory) Kirszbraun theorem (Lipschitz continuity) Kleene fixed-point theorem (order theory) Kleene's recursion theorem (recursion theory) Knaster–Tarski theorem (order theory) Kneser's theorem (combinatorics) Kneser's theorem ...
The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas in the proof sequence.