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# Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. 

## All horses are the same color

The horse paradox is a falsidical paradox that arises from flawed demonstrations, which purport to use mathematical induction, of the statement All horses are the same color.

## Anomalous cancellation

An anomalous cancellation or accidental cancellation is a particular kind of arithmetic procedural error that gives a numerically correct answer.

## Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.

## Cut-the-Knot

Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

## Difference of two squares

In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.

## Differential (mathematics)

In mathematics, differential refers to infinitesimal differences or to the derivatives of functions.

## Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

## Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

## Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

## Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

## Factorization

In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

## Fallacy

A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves" in the construction of an argument.

## Five color theorem

The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Howler (error)

A howler is a glaring blunder, typically an amusing one.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

## Integration by parts

In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.

## Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

## Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

## Lewis Carroll

Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English writer, mathematician, logician, Anglican deacon, and photographer.

## Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

## Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

## Mathematical induction

Mathematical induction is a mathematical proof technique.

## Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Multivalued function

In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.

## Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.

## Pasch's axiom

In geometry, Pasch's axiom is a statement in plane geometry, used implicitly by Euclid, which cannot be derived from the postulates as Euclid gave them.

## Principal value

In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.

## Proof by intimidation

Proof by intimidation (or argumentum verbosium) is a jocular phrase used mainly in mathematics to refer to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeal to obscure results, so that the audience is simply obliged to accept it, lest they have to admit their ignorance and lack of understanding.

## Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

## Q.E.D.

Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.

## Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

## Solution of triangles

Solution of triangles (solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known.

## Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Validity

In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

## References

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