Constructing Monotonic Sequences Converging to an Accumulation Point in a Subset of $\mathbb{R}$
Let a be a set accumulation point $A$ subset of $\mathbb{R}$. Show that there is either an increasing sequence or a decreasing sequence of points $x_n$ in A with $\lim_{n\rightarrow \infty} x_n=a$.
Mona Vinci
39
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- accepted
- 193 views
- $10.00
Related Questions
- A lower bound for an exponential series
- Limits : $x^{-1} \sin(x) $ as x -> 0 and $\tfrac{\ln(x)}{1-x}$ as x-> 0
- The space of continuous functions is a normed vector space
- real analysis
- What is the Lebesgue density of $A$ and $B$ which answers a previous question?
- Measure Theory and the Hahn Decomposition Theorem
- real analysis
- Real Analysis
