# Category:Inequalities

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This category contains results about **Inequalities**.

Definitions specific to this category can be found in Definitions/Inequalities.

An **inequality** is a mathematical statement that two expressions relate in one of several conventional ways:

- $a < b$
- $a \le b$
- $a > b$
- $a \ge b$

A statement of the form:

- $a \ne b$

may or may not be considered an **inequality**.

## Subcategories

This category has the following 28 subcategories, out of 28 total.

### B

- Bernoulli's Inequality (7 P)

### C

- Cauchy's Inequality (6 P)
- Cauchy's Mean Theorem (6 P)
- Chebyshev's Sum Inequality (7 P)

### G

- GM-HM Inequality (3 P)

### H

- Hölder's Inequality for Sums (12 P)

### J

### L

### M

### N

- Negative of Absolute Value (4 P)
- Nesbitt's Inequality (3 P)

### O

- Ordering of Reciprocals (3 P)

### R

### T

### U

### Y

## Pages in category "Inequalities"

The following 67 pages are in this category, out of 67 total.

### B

### C

### I

### M

### N

### O

### R

- Real Number between Zero and One is Greater than Power/Natural Number
- Real Number between Zero and One is Greater than Square
- Real Number Ordering is Compatible with Addition
- Real Number Ordering is Compatible with Multiplication
- Real Number Ordering is Transitive
- Real Plus Epsilon
- Reciprocal of Strictly Positive Real Number is Strictly Positive
- Relative Sizes of Definite Integrals
- Reverse Triangle Inequality
- Ring Product preserves Inequalities on Positive Elements
- Root of Number Greater than One