# Order on a number line

Wednesday, November 23rd, 2011 at
1:48 pm

## Definition of Order on a number line:

### If a and b are real numbers, a is less than b if b – a is positive.

## Inequality Symbols:

## is less than

## > is greater than

## < is less than or equal to

## is greater than or equal to

### Subsets of real numbers are called intervals.

#### a, b are the endpoints

### Bounded Intervals have 2 endpoints.

#### [a,b] Closed

#### (a,b) Open

#### [a,b)

#### (a,b]

#### More Symbols: positive infinity and negative infinity

### Unbounded Intervals have one or both endpoints that are and/or .

#### [a,)

#### (a,) Open

#### (,b]

#### (,b) Open

#### (, ) The Entire real number line

### Law of Trichotomy

#### For any two real numbers a and b, precisely one of three relationships is possible:

#### or or

**Filed under: **Pre-requisites for Pre-Calculus

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