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. See more

Inequalities are governed by the following properties. All of these properties also hold if all of the non-strict inequalities (≤ and ≥) are replaced by their … See more

The notation a < b < c stands for "a < b and b < c", from which, by the transitivity property above, it also follows that a < c. By the above laws, … See more

There are many inequalities between means. For example, for any positive numbers a1, a2, ..., an we have H ≤ G ≤ A ≤ Q, where they … See more

A (non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. That is, for all a, b, and c in P, it must satisfy the three following clauses:
1. a ≤ a (reflexivity)
2. if … See more

An inequality is said to be sharp if it cannot be relaxed and still be valid in general. Formally, a universally quantified inequality φ is called … See more

The Cauchy–Schwarz inequality states that for all vectors u and v of an inner product space it is true that See more