# JJR

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2nd year Math student

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 Aug16 comment “So That” vs. “Such That”Thank you @MarkDominus, "terminology" is a more appropriate tag Aug16 accepted Difference of two Cauchy Sequences Aug16 accepted Proof of Non-Ordering of Complex Field Aug16 accepted Format of Proof by Induction Aug16 accepted Find a sequence $\{a_n\}$ that converges to $a$ without getting “closer and closer” Aug16 asked “So That” vs. “Such That” Aug15 accepted Limit point versus limit and implications for convergence Aug15 comment Limit point versus limit and implications for convergenceSo that sequence I have constructed works as a counterexample then. Thanks @DavidMitra Aug15 comment Limit point versus limit and implications for convergenceDoes a sequence of this form "count"?: $(a_n) = 1$ for $n = 2k, k \in \mathbb N$, $(a_n) = n$ for $n = 2k - 1, k \in \mathbb N$? Aug15 asked Limit point versus limit and implications for convergence Aug15 accepted Proving that a sequence is Cauchy Aug15 comment Proving that a sequence is CauchyThanks! I see the convergent series, which gives me the $N$ I need to pick. Aug15 asked Proving that a sequence is Cauchy Aug14 comment Counterexample Check for Sum of Limit Points of SubsequencesAh ok. Thank you all for your help, I am self-studying introductory real analysis and slowly getting the hang of the material. Aug14 comment Counterexample Check for Sum of Limit Points of SubsequencesWondering @BrianM.Scott Aug14 accepted Counterexample Check for Sum of Limit Points of Subsequences Aug14 comment Counterexample Check for Sum of Limit Points of Subsequences@Rolando posted what looked like a proof of this conjecture, and then deleted it after you posted your answer. It looked something like this: Let $\epsilon >0$ be given. Since $a_n \to c$ and $b_n \to d$, there are $N_1, N_2$ such that for $l \ge N_1$, $k \ge N_2$ $|a_l - c| \le \epsilon/2$ and $|b_k - d| \le \epsilon/2$. Let $m = \max\{N_1, N_2\}$ and therefore we have for $n \ge m$ we have $|a_n - c + b_n - d| \le \epsilon$. Is the problem with his proof that he is not considering subsequences, and that he interpreted the limit points as limits? Aug14 asked Counterexample Check for Sum of Limit Points of Subsequences Aug14 accepted Convergent Subsequence in $\mathbb R$ Aug14 comment Convergent Subsequence in $\mathbb R$Never mind, of course you are right, because the denominator $\to \infty$ so the sequence $\to 0$, sorry I lost perspective. Thanks again!