What is Inequalities: Definition and 328 Discussions

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities:

The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.In either case, a is not equal to b. These relations are known as strict inequalities, meaning that a is strictly less than or strictly greater than b. Equivalence is excluded.
In contrast to strict inequalities, there are two types of inequality relations that are not strict:

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).The relation "not greater than" can also be represented by a ≯ b, the symbol for "greater than" bisected by a slash, "not". The same is true for "not less than" and a ≮ b.
The notation a ≠ b means that a is not equal to b, and is sometimes considered a form of strict inequality. It does not say that one is greater than the other; it does not even require a and b to be member of an ordered set.
In engineering sciences, less formal use of the notation is to state that one quantity is "much greater" than another, normally by several orders of magnitude. This implies that the lesser value can be neglected with little effect on the accuracy of an approximation (such as the case of ultrarelativistic limit in physics).

The notation a ≪ b means that a is much less than b. (In measure theory, however, this notation is used for absolute continuity, an unrelated concept.)
The notation a ≫ b means that a is much greater than b.In all of the cases above, any two symbols mirroring each other are symmetrical; a < b and b > a are equivalent, etc.

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  1. V

    Solving inequalities with rational expressions.

    Homework Statement Identify the solution set of the inequality. Homework Equations 5x + 1 / x- 1 ≥ 7 The Attempt at a Solution I multiplied both sides by x - 1 which gave me 5x+1 ≥ 7x - 7 Then I combined like terms together which gave me 8 ≥ 2x I divided both sides by 2 which gave...
  2. M

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  3. P

    Probabilities inequalities

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  4. S

    Can you explain the inequalities in exponential functions?

    Hello, could somebody please explain to me how 1-exp(-μt) ≤ μt and similarly (1-exp(-μt))exp(-λt) ≥ μt-μ2t2\2)(1-λt) Thanks a lot
  5. A

    Can the System of Inequalities in R be Solved with Real Numbers x, y, and z?

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  6. S

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  7. S

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  8. S

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  9. icystrike

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  10. T

    Hello Could you me demostrate some integral inequalities?

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  11. E

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  12. E

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  13. C

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  14. bohm2

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  15. E

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  16. C

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  17. JK423

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  18. T

    Inequalities with two different fractions which include x in the denominator.

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  19. P

    MHB Proving inequalities using calculus

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  20. C

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  21. T

    Solving a system of Inequalities

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  22. S

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  23. O

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  24. S

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  25. A

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  26. O

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  27. O

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  28. D

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  29. D

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  30. D

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  31. D

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  32. F

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  33. V

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  34. T

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  35. F

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  36. D

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  37. azizlwl

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  38. K

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  39. C

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  40. K

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  42. phosgene

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  43. A

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  44. phosgene

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  45. R

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  46. B

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  47. N

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  48. N

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  49. L

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  50. L

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