Question

What does bounded above or below mean in precaculus?

Answer 1

See explanation.

Explanation:

Definitions:

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

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

Examples:

Example 1

A set of natural numbers `NN` is bounded below by the number `0` or any negative number because for all natural numbers `n` we have: `0<=n` and for every negative number `N` we have `N<=n`

Example 2
Let `A` be a set `A={1/n: n in NN}`

This set can be written as `A={1, 1/2, 1/3, ...}`

This set is bounded above by `1` (or any number greater than `1`) and bounded below by `0` (or any number lower than `0`). For all `x in A` we can write that: `0<=x <=1`

Answer 2

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 .
`S = {x :x in [a,b] }` and a is less than 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 : `S={x:x in (a,b) }` and a is less than b .
still a is the lower bound and b the upper bound .