## Irrational Number Wikipedia

### Irrational number - Wikipedia.

In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers.That is, irrational numbers cannot be expressed as the ratio of two integers.When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, ....

https://en.wikipedia.org/wiki/Irrational_number.

### Rational number - Wikipedia.

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p / q of two integers, a numerator p and a non-zero denominator q. For example, -3 / 7 is a rational number, as is every integer (e.g. 5 = 5 / 1).The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by ....

https://en.wikipedia.org/wiki/Rational_number.

### Irrational Games - Wikipedia.

Irrational Games (known as 2K Boston between 2007 and 2009) was an American video game developer founded in 1997 by three former employees of Looking Glass Studios: Ken Levine, Jonathan Chey, and Robert Fermier. Take-Two Interactive acquired the studio in 2006. The studio was known for its games System Shock 2, Freedom Force, SWAT 4, and most notably, two of ....

https://en.wikipedia.org/wiki/Irrational_Games.

### Algebraic number - Wikipedia.

Examples. All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer a and a (non-zero) natural number b, satisfies the above definition, because x = a / b is the root of a non-zero polynomial, namely bx - a.; Quadratic irrational numbers, irrational solutions of a quadratic polynomial ax 2 + bx + c with integer coefficients a, b, and c, are ....

https://en.wikipedia.org/wiki/Algebraic_number.

### Square root of 2 - Wikipedia.

The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2.It may be written in mathematics as or /, and is an algebraic number.Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.. Geometrically, the square root of 2 is the length of a ....

https://en.wikipedia.org/wiki/Square_root_of_2.

### Irrationality - Wikipedia.

The term irrational is often used in psychotherapy and the concept of irrationality is especially known in rational emotive behavior therapy originated and developed by American psychologist Albert Ellis.In this approach, the term irrational is used in a slightly different way than in general. Here irrationality is defined as the tendency and leaning that humans have to act, emote and ....

https://en.wikipedia.org/wiki/Irrationality.

### Rationality - Wikipedia.

Rationality is the quality or state of being rational - that is, being based on or agreeable to reason. Rationality implies the conformity of one's beliefs with one's reasons to believe, and of one's actions with one's reasons for action. "Rationality" has different specialized meanings in philosophy, economics, sociology, psychology, evolutionary biology, game theory and political ....

https://en.wikipedia.org/wiki/Rationality.

### Negative number - Wikipedia.

In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero.Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one ....

https://en.wikipedia.org/wiki/Negative_number.

### Stockholm syndrome - Wikipedia.

Stockholm syndrome is a condition in which hostages develop a psychological bond with their captors during captivity. It results from a rather specific set of circumstances, namely the power imbalances contained in hostage-taking, kidnapping, and abusive relationships.Therefore, it is difficult to find a large number of people who experience Stockholm syndrome to conduct ....

https://en.wikipedia.org/wiki/Stockholm_syndrome.

### Ordinal number - Wikipedia.

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets.. A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used. To extend this process to various infinite sets, ordinal numbers are defined more ....

https://en.wikipedia.org/wiki/Ordinal_number.

### Cardinality - Wikipedia.

In mathematics, the cardinality of a set is a measure of the "number of elements" of the set.For example, the set = {,,} contains 3 elements, and therefore has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them..

https://en.wikipedia.org/wiki/Cardinality.

### Sexagesimal - Wikipedia.

The representations of irrational numbers in any positional number system (including decimal and sexagesimal) neither terminate nor repeat. The square root of 2 , the length of the diagonal of a unit square , was approximated by the Babylonians of the ....

https://en.wikipedia.org/wiki/Sexagesimal.

### Infinitesimal - Wikipedia.

Synthetic differential geometry or smooth infinitesimal analysis have roots in category theory.This approach departs from the classical logic used in conventional mathematics by denying the general applicability of the law of excluded middle - i.e., not (a != b) does not have to mean a = b.A nilsquare or nilpotent infinitesimal can then be defined. This is a number x where ....

https://en.wikipedia.org/wiki/Infinitesimal.

### Homophobia - Wikipedia.

It has been defined as contempt, prejudice, aversion, hatred or antipathy, may be based on irrational fear and may also be related to religious beliefs. Homophobia is ... and a number of different types have been postulated, among which are internalized homophobia, social homophobia, emotional homophobia, rationalized homophobia, ....

https://en.wikipedia.org/wiki/Homophobia.

### Quotient - Wikipedia.

A rational number can be defined as the quotient of two integers (as long as the denominator is non-zero). A more detailed definition goes as follows: A real number r is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational. Or more formally:.

https://en.wikipedia.org/wiki/Quotient.

### Hyperbolic functions - Wikipedia.

Hyperbolic tangent. The hyperbolic tangent is the (unique) solution to the differential equation f ? = 1 - f 2, with f (0) = 0.. Useful relations. The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities.In fact, Osborn's rule states that one can convert any trigonometric identity for , , or and into a hyperbolic identity, by expanding ....

https://en.wikipedia.org/wiki/Hyperbolic_functions.

### List of numbers - Wikipedia, the free encyclopedia.

A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system..

https://en.wikipedia.org/wiki/List_of_numbers.

### Proof that π is irrational - Wikipedia.

In the 1760s, Johann Heinrich Lambert was the first to prove that the number ? (pi) is irrational, meaning it cannot be expressed as a fraction /, where and are both (non-zero) integers.In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus.Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and ....

https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational.

### Decision fatigue - Wikipedia.

Definition and context. Decision fatigue is a phrase popularised by John Tierney, and is the tendency for peoples' decision making to become impaired as a result of having recently taken multiple decisions.. Decision fatigue has been hypothesised to be a symptom, or a result of ego depletion. It differs from mental fatigue which describes the psychobiological state that results ....

https://en.wikipedia.org/wiki/Decision_fatigue.

### Theory of forms - Wikipedia.

The theory of Forms or theory of Ideas is a philosophical theory, concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical ....

https://en.wikipedia.org/wiki/Theory_of_forms.

### The Enemies of Reason - Wikipedia.

The Enemies of Reason is a two-part television documentary, written and presented by evolutionary biologist Richard Dawkins, in which he seeks to expose "those areas of belief that exist without scientific proof, yet manage to hold the nation under their spell", including mediumship, acupuncture and psychokinesis.. The documentary was first broadcast on ....

https://en.wikipedia.org/wiki/The_Enemies_of_Reason.

### Leap of faith - Wikipedia.

The implication of taking a leap of faith can, depending on the context, carry positive or negative connotations, as some feel it is a virtue to be able to believe in something without evidence while others feel it is foolishness. It is a hotly contested theological and philosophical concept. For instance, the association between "blind faith" and religion is disputed by those with deistic ....

https://en.wikipedia.org/wiki/Leap_of_faith.

### Bayesian probability - Wikipedia.

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.. The Bayesian interpretation of probability can be seen as an extension of propositional logic that ....

https://en.wikipedia.org/wiki/Bayesian_probability.