What does bounded above or below mean in precaculus?

2 Answers
Apr 25, 2017

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

Apr 25, 2017

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 .