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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.
Marginal value theorem (biology, optimization) Markus−Yamabe theorem (dynamical systems) Martingale representation theorem (probability theory) Mason–Stothers theorem (polynomials) Master theorem (analysis of algorithms) (recurrence relations, asymptotic analysis) Maschke's theorem (group representations) Matiyasevich's theorem ...
compactness theorem A theorem in logic stating that if every finite subset of a set of sentences has a model, then the entire set has a model. complete infinity A concept in philosophy and mathematics referring to an actual infinity that is considered as a completed whole, contrasting with potential infinities that are indefinitely extendable.
Bet hedging (biology) Bishop–Cannings theorem; F. Fisher's fundamental theorem of natural selection; L. Lewis' law; M. Marginal value theorem; Monodomain model
The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. [3] In modern logic, an axiom is a premise or starting point for reasoning. [4] In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom".
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element ϕ ∈ T {\displaystyle \phi \in T} of a deductively closed theory T {\displaystyle T} is then called a theorem of the theory.
Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. [1] Logical truths are generally considered to be necessarily true. This is to ...
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .