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  2. Interval (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Interval_(mathematics)

    This characterization is used to specify intervals by mean of interval notation, which is described below. An open interval does not include any endpoint, and is indicated with parentheses. [2] For example, (,) = {< <} is the interval of all real numbers greater than 0 and less than 1.

  3. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    The limit, should it exist, is a positive real solution of the equation y = x y. Thus, x = y 1/y. The limit defining the infinite exponential of x does not exist when x > e 1/e because the maximum of y 1/y is e 1/e. The limit also fails to exist when 0 < x < e −e. This may be extended to complex numbers z with the definition:

  4. Interval arithmetic - Wikipedia

    en.wikipedia.org/wiki/Interval_arithmetic

    The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.

  5. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    If nonempty f: X → Y is injective, construct a left inverse g: Y → X as follows: for all y ∈ Y, if y is in the image of f, then there exists xX such that f(x) = y. Let g(y) = x; this definition is unique because f is injective. Otherwise, let g(y) be an arbitrary element of X. For all xX, f(x) is in the image of f.

  6. 68–95–99.7 rule - Wikipedia

    en.wikipedia.org/wiki/68–95–99.7_rule

    In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, [1] Χ is an observation from a normally distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: (+) % (+) % (+) %

  7. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    Thus one antiderivative, which takes the value zero for x = 1, is a differentiable function called the natural logarithm. A real function f is monotonic in an interval if the sign of () does not depend of the choice of x and y in the interval. If the function is differentiable in the interval, it is monotonic if the sign of the derivative is ...

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