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For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]
Demonstration of 2 / 3 via a zero-value game. A slight rearrangement of the series reads + + =. The series has the form of a positive integer plus a series containing every negative power of two with either a positive or negative sign, so it can be translated into the infinite blue-red Hackenbush string that represents the surreal number 1 / 3 :
Under this method, an item with a usable life of n = 4 years would lose 4 / 10 of its "losable" value in the first year, 3 / 10 in the second, 2 / 10 in the third, and 1 / 10 in the fourth, accumulating a total depreciation of 10 / 10 (the whole) of the losable value.
Pell's equation for n = 2 and six of its integer solutions. Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y.
These values can be calculated evaluating the quantile function (also known as "inverse CDF" or "ICDF") of the chi-squared distribution; [24] e. g., the χ 2 ICDF for p = 0.05 and df = 7 yields 2.1673 ≈ 2.17 as in the table above, noticing that 1 – p is the p-value from the table.
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 .
Number of isomers [3] [4] Number of isomers including stereoisomers [3] [5] Molecular Formula Name of straight chain Synonyms 1 1 1 CH 4: methane: methyl hydride; natural gas 2 1 1 C 2 H 6: ethane: dimethyl; ethyl hydride; methyl methane 3 1 1 C 3 H 8: propane: dimethyl methane; propyl hydride 4 2 2 C 4 H 10: n-butane: butyl hydride ...