What is boundedness?

1 Answer
George C.
Jun 29, 2015

Boundedness is about having finite limits. In the context of values of functions, we say that a function has an upper bound if the value does not exceed a certain upper limit. More...

Explanation:

Other terms used are "bounded above" or "bounded below".

For example, the function f(x) = 1/(1+x^2) is bounded above by 1 and below by 0 in that:

0 < f(x) <= 1 for all x in RR

graph{1/(1+x^2) [-5, 5, -2.5, 2.5]}

The function exp:x -> e^x is bounded below by 0 (or you can say has 0 as a lower bound), but is not bounded above.

0 < e^x < oo for all x in RR

graph{e^x [-5.194, 4.806, -0.74, 4.26]}

Related questions
See all questions in Boundedness
Impact of this question
10057 views around the world
You can reuse this answer
Creative Commons License