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  2. Absolute value - Wikipedia

    en.wikipedia.org/wiki/Absolute_value

    The real absolute value function is an example of a continuous function that achieves a global minimum where the derivative does not exist. The subdifferential of | x | at x = 0 is the interval [−1, 1]. [14] The complex absolute value function is continuous everywhere but complex differentiable nowhere because it violates the Cauchy–Riemann ...

  3. Ostrowski's theorem - Wikipedia

    en.wikipedia.org/wiki/Ostrowski's_theorem

    In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers is equivalent to either the usual real absolute value or a p-adic absolute value. [1]

  4. Magnitude (mathematics) - Wikipedia

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

    For numbers, the absolute value of a number is commonly applied as the measure of units between a number and zero. In vector spaces, the Euclidean norm is a measure of magnitude used to define a distance between two points in space. In physics, magnitude can be defined as quantity or distance.

  5. Markov number - Wikipedia

    en.wikipedia.org/wiki/Markov_number

    None of the prime divisors of a Markov number is congruent to 3 modulo 4, which implies that an odd Markov number is 1 more than a multiple of 4. [9] Furthermore, if m {\displaystyle m} is a Markov number then none of the prime divisors of 9 m 2 − 4 {\displaystyle 9m^{2}-4} is congruent to 3 modulo 4.

  6. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    The lowest value a function attains. absolute value The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. Namely, |x| = x for a positive x, |x| = −x for a negative x (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 ...

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  9. Absolute value (algebra) - Wikipedia

    en.wikipedia.org/wiki/Absolute_value_(algebra)

    The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).

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