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  2. Szemerédi–Trotter theorem - Wikipedia

    en.wikipedia.org/wiki/Szemerédi–Trotter_theorem

    Since each line segment lies on one of m lines, and any two lines intersect in at most one point, the crossing number of this graph is at most the number of points where two lines intersect, which is at most m(m − 1)/2. The crossing number inequality implies that either e ≤ 7.5n, or that m(m − 1)/2 ≥ e 3 / 33.75n 2.

  3. Inequality (mathematics) - Wikipedia

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

    The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.

  4. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    1.7 Number theory. 1.8 Probability theory and statistics. 1.9 Topology. ... Bell's inequality – see Bell's theorem. Bell's original inequality; CHSH inequality;

  5. Crossing number inequality - Wikipedia

    en.wikipedia.org/wiki/Crossing_number_inequality

    If there were more incidences than the Szemerédi–Trotter bound, this graph would necessarily have more crossings than the total number of pairs of lines, an impossibility. The inequality can also be used to prove Beck's theorem, that if a finite point set does not have a linear number of collinear points, then it determines a quadratic ...

  6. QM-AM-GM-HM inequalities - Wikipedia

    en.wikipedia.org/wiki/QM-AM-GM-HM_Inequalities

    The inequalities then follow easily by the Pythagorean theorem. Comparison of harmonic, geometric, arithmetic, quadratic and other mean values of two positive real numbers x 1 {\displaystyle x_{1}} and x 2 {\displaystyle x_{2}}

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  8. Linear inequality - Wikipedia

    en.wikipedia.org/wiki/Linear_inequality

    For example, [3] to draw the solution set of x + 3y < 9, one first draws the line with equation x + 3y = 9 as a dotted line, to indicate that the line is not included in the solution set since the inequality is strict. Then, pick a convenient point not on the line, such as (0,0).

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