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
- 1196 views
- $10.00
Related Questions
- Define $F : \mathbb{R}^ω → \mathbb{R}^ω$ by $F(x)_n = \sum^n_{k=1} x_k$. Determine whether $F$ restricts to give a well-defined map $F : (\ell_p, d_p) → (\ell_q, d_q)$
- Accumulation points question (Real Analysis)
- True-False real analysis questions
- Banach fixed-point theorem and the map $Tf(x)=\int_0^x f(s)ds $ on $C[0,1]$
- real analysis
- Prove that if $T \in L(V,W)$ then $ \|T\| = \inf \{M \in \R : \, \|Tv\| \le M\|v\| \textrm{ for all } v \in V \}.$
- How do we take the mean of a mathematical function using statistics?
- real analysis
