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Don't have much time these days...


Apr
17
revised how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
added 128 characters in body
Apr
11
awarded  Nice Answer
Apr
3
comment Upper bound for logarithmic integral
Based on this answer: math.stackexchange.com/a/7804/1102 (on which you commented), seems like $c=e^2 + 1$ should do.
Apr
2
revised Show that $0 < \frac{y-x}{1+xy} < 1$.
edited tags
Mar
25
comment Why is the area under a curve the integral?
@MuhammadUmer: I don't understand what you are trying to say. The second part applies here.
Mar
25
comment Why is the area under a curve the integral?
@MuhammadUmer: Because of fundamental theorem of calculus. See this:en.wikipedia.org/wiki/… (and I suggest you read the whole page).
Mar
21
revised A very challenging probability question
edited tags
Mar
19
awarded  Enlightened
Mar
19
awarded  Nice Answer
Mar
18
comment How can I solve this question?
Please, use the tex support in this site (rather than posting a image link which might rot), and choose a better title. You have been here 5 months and have asked 24 questions. You should know about these things. -1 till you fix it.
Mar
18
revised expectation of $K$ dice game
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Mar
14
revised Find $x_n$ if $x_1,x_2,\ldots,x_n$ is a set of positive numbers that satisfy $\frac{x_n+2}{2}=\sqrt{2S_n}$.
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Mar
14
revised $n$ digit integer which keeps the last $n$ digits when squared
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Mar
14
revised If $\lim_{n\to\infty}x_n=\alpha$, show $\lim_{n\to\infty}(x_1x_2\dots x_n)^{1/n} =\alpha$.
added 43 characters in body
Mar
13
comment Counterexamples in Analysis error: everywhere continuous, nowhere differentiable function
@user3821234: No, please add an actual answer and tick that. Others might have the same questions (no matter how silly you think it is). btw, your question writing skills are exemplary! (One more reason to have this question sticking around :-))
Mar
12
comment How can I explain to my professor his argument invokes the AC?
@AsafKaragila: Right, I missed the fact that the proof is talking about $B(x, r(x))$ (i.e. a ball centered at $x$, which the definition does not provide). That does need a proof. But I believe OP was claiming that the AC is used in choosing such a ball for every $x$, i.e. even if the definition were changed to "there is a ball centered at $x$...", I believe he would still have that objection. Sorry, should have read things more carefully. Thanks for taking the time to explain it.
Mar
12
comment How can I explain to my professor his argument invokes the AC?
@AsafKaragila: I was trying to talk about was a statement like this: "...space, every point has an open ball in the open set...". What does this even mean? There is a function from set of points to set of open balls? or something else? Assuming radius of an open ball is well defined, we can just compose the two. Why do we even have a choice of multiple radii? The definition only talks about the existence of a ball. I probably misunderstood the point you are trying to make, though.
Mar
12
comment How can I explain to my professor his argument invokes the AC?
@SteveKass: I would say the choice is given by the definition. The definition guarantees existence of a $B_x$ for every point $x$. Your choice function is $r(B_x)$, $r$ being the radius function. I was hoping the answers would address what defining statements like: "For every x, there is a Ball" really mean. Do they imply existence of a choice function? etc.
Mar
12
awarded  Nice Answer
Mar
12
comment Subset Sum problem computational complexity
I was talking about the individual integer value (you already gave the number of integers in the input). Your best bet might be approximation/randomized algorithms.