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23h
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
It looks OK now.
23h
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
So after "increase $\nu$ by 1", you should say "and proceed to the next $n$", or something. This is not clear from your text.
23h
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
You want to take them all? That doesn't work.
1d
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
Yes, that's clearer. Still, there are gaps. (i) Do you also require $k > k_{\nu-1}$ when you look for $a_k$? (ii) You only want to remember the first such $k$ for a given $n$, right? (iii) The special case where $a_k=L$ for all sufficiently large $k$ is not covered.
1d
comment Every sequence in $\mathbb{R}$ has a monotonic subsequence
I don't get this. What is $\nu$? Are you remembering all such $k$ for a given $n$, or just the first? In either case, your construction doesn't seem to work.
1d
revised Every sequence in $\mathbb{R}$ has a monotonic subsequence
added 3 characters in body
1d
answered Every sequence in $\mathbb{R}$ has a monotonic subsequence
1d
revised Every sequence in $\mathbb{R}$ has a monotonic subsequence
deleted 2 characters in body
1d
comment Maximising the Area of a Cyclic Quadrilateral
You seem to have swapped $C$ and $D$. I have edited your answer to put them right; let me know if I have misread your intentions.
1d
revised Maximising the Area of a Cyclic Quadrilateral
Unswapped $C$ and $D$
2d
awarded  Constituent
2d
comment 2014 Fall OMO #28
And an OMO is...?
2d
comment What is the cardinality of the following equivalence classes?
@Robert: That is the Continuum Hypothesis! You certainly don't need CH to prove that $\mathbb R/\pi\mathbb Q$ has the same cardinality as $\mathbb R$.
2d
comment What is the cardinality of the following equivalence classes?
@Greentree1912: Because the number of such classes is uncountable.
Dec
18
revised Show that $\{e^{in}: n\in\Bbb N\}$ is Dense in the Unit Circle
added 2 characters in body
Dec
18
comment How to visualize $f(x) = (-2)^x$
Here is a related question.
Dec
18
answered Show that $\{e^{in}: n\in\Bbb N\}$ is Dense in the Unit Circle
Dec
17
comment How to explain to a layman why Fermat's Last Theorem involves non-trivial math?
"it is sufficient to prove FLT($p$) for every prime $p$": You mean, "it is sufficient to prove FLT($p$) for every odd prime $p$, and FLT($n$) for $n=4$."
Dec
16
comment Is this two-dimensional version of the Intermediate Value Theorem correct?
Can anybody make sense of this?
Dec
16
comment Engineering - Appropriate concrete grade for supporting structure under wind loading?
I would say you've come to the wrong place with this question. We do abstract here, not concrete.