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 $\lim_{n\rightarrow \infty} x_n=a$.
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
- 1153 views
- $10.00
Related Questions
- Find $\lim _{x \rightarrow 0^{+}} \sqrt{x}\ln x$
- Prove Holder-continuity for $\mu_\lambda (x) = \sum\limits_{n=1}^\infty \frac{ \cos(2^n x)}{2^{n \lambda} }$
- real analysis
- Calculating P values from data.
- Prove that a closed subset of a compact set is compact.
- Probability Question
- Compute $\lim_{x \rightarrow 0} \frac{1-\arctan (\sin(x)+1)}{e^{x}-1}$
- Suppose that $T \in L(V,W)$. Prove that if Img$(T)$ is dense in $W$ then $T^*$ is one-to-one.