> Definition. We define a continuous sequence to be a real valued function f defined
on the open interval [0, 1) such that there exists a real number c for which f(x) ≤ c
for all x ∈ [0, 1).
on the open interval [0, 1) such that there exists a real number c for which f(x) ≤ c
for all x ∈ [0, 1).
If the function $f$ is defined on an unbounded above domain $D \subseteq \Re $ and is eventually monotone and eventually bounded, then $ \lim_{x\rightarrow \infty} f(x)$ is finite
I tried to workout the proof as:
Since $f$ is eventually monotone $\Rightarrow \exists x^*, x^* \leq x_1 < x_2 $ we...
