If \(f(X)\) is not bounded, (i.e. not bounded above or it is not bounded below or neither bounded above nor bounded below), we call \(f\) unbounded.
1 Please note that $X$ does not necessarily have to be a subset of real numbers $\mathbb R$. The concept of bounded functions can be defined more generally for any kind sets. The only important detail is that the image set of the function is a subset of $\mathbb R$.
| | | | | created: 2014-02-21 20:55:03 | modified: 2020-01-24 08:57:10 | by: bookofproofs | references: 
 Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983