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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. [1]

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 is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

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, the term differential has several meanings.

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 called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry".

Euclidean geometry

Euclidean geometry is a mathematical system attributed to the 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 is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

Fallacy

A fallacy is the use of poor, or invalid, reasoning for 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 and computer science, 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 term imaginary unit or unit imaginary number refers to a solution to the equation.

Informal fallacy

An informal fallacy occurs in an argument whose stated premises may fail to adequately support its proposed conclusion.

Integral

The integral is an important concept in mathematics.

Integration by parts

In calculus, and more generally in mathematical analysis, integration by parts is a theorem that relates the integral of a product of functions to the integral of their derivative and antiderivative.

Inverse function

In mathematics, an inverse function is a function that "reverses" another function.

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 method of mathematical proof typically used to establish a given statement for all natural numbers.

Mathematical proof

In mathematics, a proof is a deductive argument for a mathematical statement.

Mathematics

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

Multivalued function

In mathematics, a multivalued function (short form: multifunction; other names: many-valued function, set-valued function, set-valued map, point-to-set map, multi-valued map, multimap, correspondence, carrier) is a left-total relation (that is, every input is associated with at least one output) in which at least one input is associated with multiple (two or more) outputs.

Nth root

In mathematics, the nth root of a number x, where n is 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 apparently contradicts itself and yet might be true (or wrong at the same time).

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.

Polynomial greatest common divisor

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.

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 relation in Euclidean geometry among the three sides of a right triangle.

Q.E.D.

Q.E.D. is an initialism of the Latin phrase quod erat demonstrandum, originating from the Ancient Greek analogous hóper édei deîxai (ὅπερ ἔδει δεῖξαι), meaning "which is what had to be proven".

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 historical term for solving 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.

Truth

Truth is most often used to mean being in accord with fact or reality,Merriam-Webster's Online Dictionary,, 2005 or fidelity to an original or to a standard or ideal.

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 In other words, a "zero" of a function is an input value that produces an output of zero (0).

References

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