What does bounded above or below mean in precaculus?

2 Answers
Apr 25, 2017

Answer:

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

Answer:

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 .