Search results
Results from the WOW.Com Content Network
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
In classical logic, disjunctive syllogism[1][2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5][6] An example in English: I will choose soup or I will choose salad. I will not choose soup.
Proof by example. In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. [1][2] The structure, argument form and formal form of a proof by example generally ...
In propositional logic, modus tollens (/ ˈmoʊdəsˈtɒlɛnz /) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away") [ 2 ] and denying the consequent, [ 3 ] is a deductive argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q.
Colloquial use of "mathematical proof". [edit] The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical.
Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used to indicate the assumption that what follows is chosen arbitrarily, narrowing the premise to a particular case, but does ...
The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function application : if f is a function of type P → Q and x ...
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen [1] as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively).