# What does bounded above or below mean in precaculus?

##### 2 Answers

See explanation.

#### Explanation:

Definitions:

A set is **bounded above** by the number *higher* than or equal to all elements of the set.

A set is **bounded below** by the number *lower* than or equal to all elements of the set.

Examples:

**Example 1**

A set of natural numbers **bounded below** by the number

**Example 2**

Let

This set can be written as

This set is **bounded above** by **bounded below** by

suppose you have a set S .

#### Explanation:

Suppose you have a set of values containing values between a real number a and b including a and b .

each value in above mentioned set of values is more than or equal to a and similarly, each value is less than or equal to b.

Thus the set is said to be bounded , where ,

a is said to be the lower bound of set and b the upper bound of set .

if the set is :

still a is the lower bound and b the upper bound .