Ad
related to: contrary and contradictory difference definition geometry math terms pdf
Search results
Results from the WOW.Com Content Network
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...
Italian school of algebraic geometry. Most gaps in proofs are caused either by a subtle technical oversight, or before the 20th century by a lack of precise definitions. A major exception to this is the Italian school of algebraic geometry in the first half of the 20th century, where lower standards of rigor gradually became acceptable.
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
A categorical proposition is a simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject. Every categorical proposition can be reduced to one of four logical forms , named A , E , I , and O based on the Latin a ff i rmo (I affirm), for the affirmative propositions ...
In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that
Other terms, such as "circle", have their meanings tacitly changed to work in complex projective space; for example, a circle in complex algebraic geometry is a conic passing through the circular points at infinity and has underlying topological space a 2-sphere rather than a 1-sphere.
Ad
related to: contrary and contradictory difference definition geometry math terms pdf