Inequality (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 13/01/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Inequality_(mathematics)


00:02:30 1 Properties
00:02:53 1.1 Transitivity
00:03:46 1.2 Converse
00:03:52 1.3 Addition and subtraction
00:04:15 1.4 Multiplication and division
00:04:53 1.5 Additive inverse
00:05:32 1.6 Multiplicative inverse
00:05:58 1.7 Applying a function to both sides
00:06:49 2 Ordered fields
00:08:14 3 Chained notation
00:09:09 4 Sharp inequalities
00:09:17 5 Inequalities between means
00:10:10 6 Power inequalities
00:10:20 6.1 Examples
00:11:01 7 Well-known inequalities
00:11:22 8 Complex numbers and inequalities
00:11:49 9 Vector inequalities
00:17:54 10 General existence theorems
00:18:18 11 See also
00:21:32 12 References
00:26:42 13 External links
00:28:55 See also



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SUMMARY
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In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).

The notation a ≠ b means that a is not equal to b.It does not say that one is greater than the other, or even that they can be compared in size.If the values in question are elements of an ordered set, such as the integers or the real numbers, they can be compared in size.

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. The notation a  b may also be read as "a is strictly less than b".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, not greater than b, or at most b); "not greater than" can also be represented by a ≯ b, the symbol for "greater than" bisected by a vertical line, "not". (The Unicode characters are: U+2264 ≤ LESS-THAN OR EQUAL TO, U+2A7D ⩽ LESS-THAN OR SLANTED EQUAL TO, and U+226F ≯ NOT GREATER-THAN.)
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, not less than b, or at least b); "not less than" can also be represented by a ≮ b, the symbol for "less than" bisected by a vertical line, "not". (The Unicode characters are: U+2265 ≥ GREATER-THAN OR EQUAL TO, U+2A7E ⩾ GREATER-THAN OR SLANTED EQUAL TO, and U+226E ≮ NOT LESS-THAN.)In engineering sciences, a 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.  (For example, the 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.