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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 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 ...
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]
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.
Cor – corollary. corr – correlation. cos – cosine function. cosec – cosecant function. (Also written as csc.) cosech – hyperbolic cosecant function. (Also written as csch.) cosh – hyperbolic cosine function. cosiv – coversine function. (Also written as cover, covers, cvs.) cot – cotangent function. (Also written as ctg.)
In mathematics and other fields, [a] a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem".
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.
It is a corollary of Gödel's incompleteness theorem that there is no deductive system (that is, no notion of provability) for second-order formulas that simultaneously satisfies these three desired attributes: [d] Every provable second-order sentence is universally valid, i.e., true in all domains under standard semantics.