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The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1] For example, the constant π may be defined as the ratio of the length of a circle's circumference to ...
Pages in category "e (mathematical constant)" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. ...
Euler's identity is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof [ 3 ] [ 4 ] that π is transcendental , which implies the impossibility of squaring the circle .
The constant e also has applications to probability theory, where it arises in a way not obviously related to exponential growth. As an example, suppose that a slot machine with a one in n probability of winning is played n times, then for large n (e.g., one million), the probability that nothing will be won will tend to 1/e as n tends to infinity.
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As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings: A fixed and well-defined number or other non-changing mathematical object, or the symbol denoting it. [1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning ...