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<B> [[Euler's constant|Euler's constant]]</B>: The limit, as <math>n</math> approaches infinity, of | <B> [[Euler's constant|Euler's constant]]</B>: The limit, as <math>n</math> approaches infinity, of | ||
:<math>1 + \frac{1}{2} + | :<math>1 + \frac{1}{2} + … + \frac{1}{n} - \text{In} n</math> | ||
It is usually denoted by 'y and its numerical value is 0.5772l56649... . | It is usually denoted by 'y and its numerical value is 0.5772l56649... . | ||
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<B> [[Exchangeable|Exchangeable]]; [[exchangeability|exchangeability]]</B>: Let <math>X_l, X_2, X_3 | <B> [[Exchangeable|Exchangeable]]; [[exchangeability|exchangeability]]</B>: Let <math>X_l, X_2, X_3 … </math>, be an infinite sequence of [[random variable]]s. If it is the case that, for all values of <math>m</math>, any two sets of <math>m</math> variables have the same joint *distribution as one another, then the sequence is said to be exchangeable and to display exchangeability. The term was introduced by *de Finetti in the early 1930s. | ||
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:<math>e^x = 1+ x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...</math> | :<math>e^x = 1+ x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...</math> | ||
The notation reflects the index property that <math>e^x \times e^y = e^{x+y}</math>. The notation 'exp<math>(x)</math>’ is sometimes used for <math>e^x</math>, particularly when <math>x</math> is a complicated algebraic expression. The number e is given by the above series with <math>x = 1</math>, so | The notation reflects the index property that <math>e^x \times e^y = e^{x+y}</math>. The notation 'exp<math>(x)</math>’ is sometimes used for <math>e^x</math>, particularly when <math>x</math> is a complicated algebraic expression. The number e is given by the above series with <math>x = 1</math>, so | ||
:<math>e = 1 + 1 + \frac{1}{2!} + \frac{1}{3!} + | :<math>e = 1 + 1 + \frac{1}{2!} + \frac{1}{3!} + … \approx 2.71828.</math> | ||
The exponential and *natural logarithm functions are related by exp<math>(ln x) = x</math> for <math>x > 0</math> and In<math>(e^x) = x</math> for all values of <math>x</math>. | The exponential and *natural logarithm functions are related by exp<math>(ln x) = x</math> for <math>x > 0</math> and In<math>(e^x) = x</math> for all values of <math>x</math>. | ||