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  2. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    Big M method. In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints. It does so by associating the constraints with large negative constants which would not be part of any optimal ...

  3. Absolute value - Wikipedia

    en.wikipedia.org/wiki/Absolute_value

    The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...

  4. Inequality (mathematics) - Wikipedia

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

    For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < ⁠ 1 / 2 ⁠ and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < ⁠ 1 / 2 ⁠.

  5. Absolute difference - Wikipedia

    en.wikipedia.org/wiki/Absolute_difference

    The absolute difference of two real numbers and is given by , the absolute value of their difference. It describes the distance on the real line between the points corresponding to and . It is a special case of the L p distance for all and is the standard metric used for both the set of rational numbers and their completion, the set of real ...

  6. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek ...

  7. Cauchy–Schwarz inequality - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

    Cauchy–Schwarz inequality (Modified Schwarz inequality for 2-positive maps [27]) — For a 2-positive map between C*-algebras, for all , in its domain, () ‖ ‖ (), ‖ ‖ ‖ ‖ ‖ ‖. Another generalization is a refinement obtained by interpolating between both sides of the Cauchy–Schwarz inequality:

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  9. Baker's theorem - Wikipedia

    en.wikipedia.org/wiki/Baker's_theorem

    Baker's Theorem — If , …, are linearly independent over the rational numbers, then for any algebraic numbers , …,, not all zero, we have | + + + | > where H is the maximum of the heights of and C is an effectively computable number depending on n, and the maximum d of the degrees of . (If β 0 is nonzero then the assumption that are linearly independent can be dropped.)

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