## Pot calling the kettle black

The pot calling the kettle black is an informal fallacy also called Tu quoque. Another name is appeal to hypocrisy. It happens when a person is guilty of the very thing of which they accuse another. A fable, perhaps by Aesop, has a mother crab an ...

## Red herring

A red herring is something that misleads or distracts from an issue. There are two ways in which it is used. One, it may be used as logical fallacy during an argument so that someone arguing does not have to answer a difficult question. For examp ...

Reductio ad Hitlerum, also known as playing the Hitler card, is a logical fallacy described by Leo Strauss, a philosopher, in 1951. It happens when someone compares their opponents view with Hitler or something that he did. It is a form of ad hom ...

## Slippery slope

The slippery slope argument is an argument that a small step will or must lead to a certain chain of events. The hypothetical chain of events leads to a significant result. So unintended consequences follow the first step in the chain of events. ...

## Straw man

Straw man is a device or trope used in arguments. The phrase describes a misrepresentation or false version of an argument. This is an informal fallacy. The reasoning is flawed because it distorts issues. A false version of the other sides argume ...

## Sunk cost fallacy

A sunk cost fallacy is a fallacy where someone convinces themselves that they should continue doing something because they put in a lot of time and/or effort into it, even if they actually get very little reward out of it. For example, a person m ...

## Two wrongs make a right

The phrases, Two wrongs make a right and two wrongs dont make a right are English phrases that denote philosophical norms. The key idea is based on the two wrongs phrase which consider the two things as wrong. Two wrongs dont make a right”, is a ...

A paradox is a sentence in logic that cannot be true but also cannot be false. It is self-contradictory. Many famous problems of this kind exist. A famous paradox is called the liars paradox. It is the simple sentence "This sentence is a lie", or ...

## Prisoners dilemma

The prisoners dilemma is a paradox about co-operation. It shows why two "rational" individuals might not co-operate, even if it seems in their best interests. It is studied in game theory.

## Ship of Theseus

The ship of Theseus is a question about if you can consider that an object is the same one when you replace parts of it. It is a paradox. For example, if you have an axe and you replace its handle, it is still the same axe? And if you replace the ...

## Rule of inference

In logic, a rule of inference, inference rule, or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion. For example, the rule of inference called modus ponens takes t ...

## Modus ponens

Modus ponendo ponens is a valid, simple argument form in classical logic sometimes referred to as affirming the antecedent or the law of detachment. It is closely related to another valid form of argument, modus tollens or denying the consequent. ...

## Modus tollens

Modus tollendo tollens is a valid, simple argument form in classical logic. It is referred to as denying the consequent. It is closely related to another valid form of argument, modus ponens or affirming the antecedent. Modus tollens is a very co ...

## −1 (number)

In mathematics, −1 is the additive inverse of 1. That is, if it is added to 1, the result is 0. It is the negative integer greater than negative two and less than 0. Negative one has some similar properties as positive one. But some are different ...

## 1 (number)

One is a natural number after zero and before two. It represents a single item. A human typically has one head, nose, mouth, and navel. The Roman numeral for one is I.

## 103 (number)

## 108 (number)

## 2 (number)

Two has many meanings in math. For example: 1 + 1 = 2 {\displaystyle 1+1=2}. An integer is even if half of it equals an integer. If the last digit of a number is even, then the number is even. This means that if you multiply 2 times anything, it ...

## 20 (number)

Twenty is the number that is after nineteen and before twenty-one. The prime factors of twenty are 2 and 5. 2 * 2 * 5 = 20 Its factors are: 1, 2, 4, 5, 10, and 20. As the sum of its factors is more than itself i.e. 22, it can be referred to as an ...

## 2047 (number)

## 243 (number)

## 6000 (number)

## 777 (number)

## Googol

A googol is the number 10 100. A 9-year-old Milton Sirotta, nephew of U.S. mathematician Edward Kasner, first used the word googol. Sirotta made this word in 1937, for the number represented by the numeral 1 followed by 100 zeros. The company Goo ...

## Million

One million, or one thousand thousand, is the natural number after 999.999 and before 1.000.001. The name is derived from Italian, where mille was 1.000, and 1.000.000 became a milione ", as a large thousand. In scientific notation, the number is ...

## Zero

Zero is a special number. If there are zero things, then there is nothing at all. For example, if a person has zero hats, that means they do not have any hats.

## E (mathematical constant)

e is a number. It is the base of natural logarithm and is about 2.71828. It is an important mathematical constant. The number e is occasionally called Eulers number after the Swiss mathematician Leonhard Euler, or Napiers constant in honor of the ...

## Golden ratio

With one number a and another smaller number b, the ratio of the two numbers is found by dividing them. Their ratio is a / b. Another ratio is found by adding the two numbers together and dividing this by the larger number a. The new ratio is / a ...

## Square root of 2

The square root of 2, or the th power of 2, written in mathematics as √ 2 or 2 ​ 1 ⁄ 2, is the positive irrational number that, when multiplied by itself, equals the number 2. To be more correct, it is called the principal square root of 2, to te ...

## Complex number

A complex number is a number, but is different from common numbers in many ways. A complex number is made up using two numbers combined together. The first part is a real number, and the second part is an imaginary number. The most important imag ...

## Fermat number

A Fermat number is a special positive number. Fermat numbers are named after Pierre de Fermat. The formula that generates them is F n = 2 n + 1 {\displaystyle F_{n}=2^{2^{\overset {n}{}}}+1} where n is a nonnegative integer. The first nine Fermat ...

## Fermats Last Theorem

Fermats Last Theorem is a very famous idea in mathematics. It says that: If n {\displaystyle n} is a whole number larger than 2, then the equation x n + y n = z n {\displaystyle x^{n}+y^{n}=z^{n}} has no solutions when x, y and z are natural numb ...

## Fundamental theorem of arithmetic

The Fundamental theorem of arithmetic is a theorem of number theory. The theorem says that every positive integer greater than 1 can be written as a product of prime numbers. The theorem also says that there is only one way to write the number. I ...

## Imaginary number

Imaginary numbers are numbers that are made from combining a real number with the imaginary unit, called i, where i is defined as i 2 = − 1 {\displaystyle i^{2}=-1}. They are defined separately from the negative real numbers in that they are a sq ...

## Iwasawa theory

In number theory, Iwasawa theory is a Galois module theory of ideal class groups, started by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur thought about generalizations of Iwasawa theo ...

## Negative number

A negative number is a number that indicates an opposite. For example: If a positive number is distance up, then a negative number is distance down. If a positive number means addition, then a negative number means subtraction. If a positive numb ...

## Parity of zero

Parity of zero is the question whether the number zero is even or odd. General consensus is that the number is even. Even numbers are defined to be integer multiples of two. That way, the numbers two, four and six are even, because they are one t ...

## Perfect number

A number is called a perfect number if by adding all the positive divisors of the number, the result is the number itself. 6 is the first perfect number. Its divisors other than the number itself: 6 are 1, 2, and 3 and 1 + 2 + 3 equals 6. Other p ...

## Prime number theorem

The prime number theorem is a theorem from number theory. Prime numbers are not distributed evenly across the number range. The theorem formalizes the idea that the probability of hitting a prime number between 1 and a given number becomes smalle ...

## Real number

A real number is a rational or irrational number, and is a number which can be expressed using decimal expansion. Usually when people say "number", they usually mean "real number". The official symbol for real numbers is a bold R, or a blackboard ...

## Sophie Germain prime

A Sophie Germain prime is a type of prime number. If a prime number is still prime after being multiplied by 2 and adding 1 to the answer, then the original prime is a Sophie Germain prime. A mathematical definition is: a prime number, denoted by ...

## Square number

A square number, sometimes also called a perfect square, is the result of an integer multiplied by itself. 1, 4, 9, 16 and 25 are the first five square numbers. In a formula, the square of a number n is denoted n 2, usually pronounced as n square ...

## Taxicab number

A taxicab number is the name given by mathematicians to a sequence of special numbers: 2, 1729 etc. A taxicab number is the smallest number that can be expressed as the sum of two positive cubes in n distinct ways. It has nothing to do with taxis ...

## Gaussian distribution

## Gumbel distribution

The Gumbel distribution is a probability distribution of extreme values. In probability theory and statistics, the Gumbel distribution is used to model the distribution of the maximum or the minimum of a number of samples of various distributions ...

## Maxwell–Boltzmann distribution

In statistics the Maxwell–Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used in physics for describing particle speeds in idealized gases. In an idea ...

## Gaussian distribution

The normal distribution is a probability distribution. It is also called Gaussian distribution because it was first discovered by Carl Friedrich Gauss. The normal distribution is a continuous probability distribution that is very important in man ...

## Pareto distribution

The Pareto distribution is a probability distribution named after Vilfredo Pareto. It is continuous and follows a power law. It is a heavy tailed distribution. The Pareto distribution was first used to show how income is distributed among househo ...

## Students t-distribution

Students t-distribution is a probability distribution which was developed by William Sealy Gosset in 1908. Student is the pseudonym he used when he published the paper describing the distribution. A normal distribution describes a full population ...