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  2. Inequation - Wikipedia

    en.wikipedia.org/wiki/Inequation

    In mathematics, an inequation is a statement that an inequality holds between two values. [1] [2] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:

  3. 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}}

  4. Cauchy–Schwarz inequality - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

    It is considered one of the most important and widely used inequalities in mathematics. [5] Inner products of vectors can describe finite sums (via finite-dimensional vector spaces), infinite series (via vectors in sequence spaces), and integrals (via vectors in Hilbert spaces). The inequality for sums was published by Augustin-Louis Cauchy .

  5. 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 ⁠.

  6. Chemical reaction - Wikipedia

    en.wikipedia.org/wiki/Chemical_reaction

    On the other hand, the chlorine gas goes from an oxidation of 0 (also a pure element) to −1: the chlorine gains one electron and is said to have been reduced. Because the chlorine is the one reduced, it is considered the electron acceptor, or in other words, induces oxidation in the sodium – thus the chlorine gas is considered the oxidizing ...

  7. Titu's lemma - Wikipedia

    en.wikipedia.org/wiki/Titu's_Lemma

    In mathematics, the following inequality is known as Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful inequality of Nairi Sedrakyan published in 1997, [1] to the book Problem-solving strategies of Arthur Engel published in 1998 and to the book Mathematical Olympiad Treasures of Titu ...

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