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In mathematics, a corollary is a theorem connected by a short proof to an existing theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof.
A porism is a mathematical proposition or corollary. It has been used to refer to a direct consequence of a proof, analogous to how a corollary refers to a direct consequence of a theorem. In modern usage, it is a relationship that holds for an infinite range of values but only if a certain condition is assumed, such as Steiner's porism. [1]
corollary A proposition that follows directly from another proposition or theorem with little or no additional proof. correspondence theory of truth The philosophical doctrine that the truth or falsity of a statement is determined by how it relates to the world and whether it accurately describes (corresponds with) that world. counterexample 1.
A corollary is a proposition that follows immediately from another theorem or axiom, with little or no required proof. [14] A corollary may also be a restatement of a theorem in a simpler form, or for a special case : for example, the theorem "all internal angles in a rectangle are right angles " has a corollary that "all internal angles in a ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
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 of a deductively closed theory is then called a theorem of the theory.
Classical logic is the standard logic of mathematics. Many mathematical theorems rely on classical rules of inference such as disjunctive syllogism and the double negation elimination. The adjective "classical" in logic is not related to the use of the adjective "classical" in physics, which has another meaning.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).