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Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation a n + b n = c n for any integer value of n greater than 2. (For n equal to 1, the equation is a linear equation and has a solution for every possible a and b. For n equal to 2, the equation has infinitely many solutions, the Pythagorean triples.)
Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. [2] Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
Ramanujan–Skolem's theorem (Diophantine equations) Ramsey's theorem (graph theory, combinatorics) Rank–nullity theorem (linear algebra) Rao–Blackwell theorem ; Rashevsky–Chow theorem (control theory) Rational root theorem (algebra, polynomials) Rationality theorem ; Ratner's theorems (ergodic theory)
Scientific WorkPlace (often abbreviated to SWP) is a software package for scientific word processing on Microsoft Windows and macOS.. Although advertised as a WYSIWYG LaTeX-based word processor, it is actually a graphical user interface for editing LaTeX source files with the same ease-of-use of a word processor, while maintaining a screen view that resembles but is not identical to the ...
Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester.Up to Version 3, it was developed by Andrei Voronkov together with Kryštof Hoder and previously with Alexandre Riazanov.
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
theorem and_swap (p q : Prop) : p ∧ q → q ∧ p := by intro h -- assume p ∧ q with proof h, the goal is q ∧ p apply And.intro -- the goal is split into two subgoals, one is q and the other is p · exact h.right -- the first subgoal is exactly the right part of h : p ∧ q · exact h.left -- the second subgoal is exactly the left part of ...