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The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, always equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional ...
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than > greater than; ≤ less than or equal to; ≥ greater than or equal to; ≠ not equal to; A linear inequality looks exactly like a linear equation, with the inequality sign ...
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 .
A set equipped with a total order is a totally ordered set; [5] the terms simply ordered set, [2] linearly ordered set, [3] [5] toset [6] and loset [7] [8] are also used. The term chain is sometimes defined as a synonym of totally ordered set , [ 5 ] but generally refers to a totally ordered subset of a given partially ordered set.
In mathematics, an ordered algebra is an algebra over the real numbers with unit e together with an associated order such that e is positive (i.e. e ≥ 0), the product of any two positive elements is again positive, and when A is considered as a vector space over then it is an Archimedean ordered vector space.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]