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  2. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. [ 124 ] [ 125 ] The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". [ 14 ]

  3. Cyclic number - Wikipedia

    en.wikipedia.org/wiki/Cyclic_number

    Let t = 0. Let r = 1. Let n = 0. loop: Let t = t + 1 Let x = r ⋅ b Let d = int(x / p) Let r = x mod p Let n = n ⋅ b + d If r ≠ 1 then repeat the loop. if t = p − 1 then n is a cyclic number. This procedure works by computing the digits of 1/p in base b, by long division. r is the remainder at each step, and d is the digit produced. The ...

  4. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Tangent line at (x 0, f(x 0)). The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point. Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a ...

  5. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi , whose real part is zero. It is common to write a + 0 i = a , 0 + bi = bi , and a + (− b ) i = a − bi ; for example, 3 + (−4) i = 3 − 4 i .

  6. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

  7. Field (mathematics) - Wikipedia

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

    In particular, one may deduce the additive inverse of every element as soon as one knows −1. [9] If ab = 0 then a or b must be 0, since, if a ≠ 0, then b = (a −1 a)b = a −1 (ab) = a −10 = 0. This means that every field is an integral domain. In addition, the following properties are true for any elements a and b: −0 = 0 11 ...

  8. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    For example, with z = 1.5 the third approximation yields 0.4167, which is about 0.011 greater than ln(1.5) = 0.405465, and the ninth approximation yields 0.40553, which is only about 0.0001 greater. The n th partial sum can approximate ln( z ) with arbitrary precision, provided the number of summands n is large enough.

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