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A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
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. In many cases, a corollary corresponds to a special case of a larger theorem, [4] which makes the theorem easier to use and apply, [5] even though its importance is generally considered to be secondary to that of ...
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]
The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: not (A or B) = (not A) and (not B) not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning at least one of A or B rather than an "exclusive or" that means exactly one of A or B.
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 ...
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
The Rule of 72 is an estimate, and more accurate at around 8 percent interest. The further the interest rate or inflation rate is from 8 percent, the less precise the result will be.
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.