Question

What is boundedness?

Answer 1

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]}