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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.
Geometric mean theorem ; Geroch's splitting theorem (differential geometry) Gershgorin circle theorem (matrix theory) Gibbard–Satterthwaite theorem (voting methods) Girsanov's theorem (stochastic processes) Glaisher's theorem (number theory) Gleason's theorem (Hilbert space) Glivenko's theorem (mathematical logic) Glivenko's theorem (probability)
Löb's theorem A theorem in mathematical logic that provides conditions under which a statement about its own provability is provable, related to Gödel's incompleteness theorems. logic The systematic study of the form of valid inference, including the structures that allow or compel particular conclusions given certain premises. logic gate
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.
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 .
In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants. Logical constants determine whether a statement is a logical truth when they are combined with a language that limits its meaning.
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
Logic studies valid forms of inference like modus ponens. Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and ...