Suppose that $f:\mathbb R\longrightarrow\mathbb [0,+\infty[$ is an unlimited function. For every $n\in\mathbb N$ let's define the function $f_n(x)=\min\{f(x),n\}$, now my question is the following:
Does the sequence $\{f_n\}$ converge uniformly to $f$ in $\mathbb R$?
Intuitively the answer seems to be YES but in the effective calculations there are some indeterminate forms such as $\infty -\infty.$