meta user
network profile
| bio | website | |
|---|---|---|
| location | ||
| age | 20 | |
| visits | member for | 11 months |
| seen | 27 mins ago | |
| stats | profile views | 193 |
2nd year Math student
Avid tennis player
Mahler aficionado
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Aug 16 |
comment |
“So That” vs. “Such That” Thank you @MarkDominus, "terminology" is a more appropriate tag |
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Aug 16 |
accepted | Difference of two Cauchy Sequences |
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Aug 16 |
accepted | Proof of Non-Ordering of Complex Field |
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Aug 16 |
accepted | Format of Proof by Induction |
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Aug 16 |
accepted | Find a sequence $\{a_n\}$ that converges to $a$ without getting “closer and closer” |
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Aug 16 |
asked | “So That” vs. “Such That” |
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Aug 15 |
accepted | Limit point versus limit and implications for convergence |
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Aug 15 |
comment |
Limit point versus limit and implications for convergence So that sequence I have constructed works as a counterexample then. Thanks @DavidMitra |
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Aug 15 |
comment |
Limit point versus limit and implications for convergence Does a sequence of this form "count"?: $(a_n) = 1$ for $n = 2k, k \in \mathbb N$, $(a_n) = n$ for $n = 2k - 1, k \in \mathbb N$? |
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Aug 15 |
asked | Limit point versus limit and implications for convergence |
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Aug 15 |
accepted | Proving that a sequence is Cauchy |
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Aug 15 |
comment |
Proving that a sequence is Cauchy Thanks! I see the convergent series, which gives me the $N$ I need to pick. |
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Aug 15 |
asked | Proving that a sequence is Cauchy |
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Aug 14 |
comment |
Counterexample Check for Sum of Limit Points of Subsequences Ah ok. Thank you all for your help, I am self-studying introductory real analysis and slowly getting the hang of the material. |
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Aug 14 |
comment |
Counterexample Check for Sum of Limit Points of Subsequences Wondering @BrianM.Scott |
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Aug 14 |
accepted | Counterexample Check for Sum of Limit Points of Subsequences |
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Aug 14 |
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? |
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Aug 14 |
asked | Counterexample Check for Sum of Limit Points of Subsequences |
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Aug 14 |
accepted | Convergent Subsequence in $\mathbb R$ |
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Aug 14 |
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! |
