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Nov
8
comment Norm in R^2 in which norm(abs(x)) != norm(x)
@Martín-BlasPérezPinilla OK, so you're saying norm(a) means a is a member of R^2 whereas abs(a) means a is a member of R? I think you're right. I was treating (x,y) in R^2 as x+i*y
Nov
8
comment Norm in R^2 in which norm(abs(x)) != norm(x)
@Martín-BlasPérezPinilla But the norm is also a real number. To answer this, I'd have to look up the definition of norm, and see if something like max(x,y) counts. However, I'm too lazy to do this :) Or did you mean that you can only take the absolute value of real numbers, not points in R^2?
Nov
3
comment Conceptual question on showing properties of the absolute value function on $\mathbb{Q}$
OK, I might be misunderstanding the question, but if |a|=0 then a=+0 or a=-0, which are the same thing. I don't see this as a rational number question. It's true for natural numbers, integers, real numbers, and complex numbers as well.
Nov
3
comment Confidence Interval for a Mean
Nah, I'm bad about upvoting other people's answers to my questions, so I feel bad about getting upvotes :)
Nov
3
comment Conceptual question on showing properties of the absolute value function on $\mathbb{Q}$
Could you show us a more complicated example that doesn't have a simple proof like this one?
Nov
3
comment Confidence Interval for a Mean
For a sample size this small, perhaps use the Student T distribution instead?
Nov
2
comment Working out percentage from Normal Distribution
(1-0.8849) is the probability of z>=1.2, not z<=1.2
Nov
1
comment Properties of continuity
You can also do this directly: to prove continuity at a point k, take c=k-epsilon and d=k+epsilon as epsilon approaches zero and then apply continuity.
Oct
29
comment Normal Distribution and Cofffee
Remember, you're looking at cumulative probability, not just the probability at a specific integer. Add the probabilities (starting with x=3) until the exceed 0.5. There's actually probably a better way of doing this, but this method will work too.
Oct
29
comment Normal Distribution and Cofffee
Hint: you're looking for 3 or more successes (well, failures, but still) in n attempts, where each success has a 1% chance. Use either the binomial distribution (or the normal approximation to it) to find the value of n where the probability is right around 0.5. Other hint: 3 or more successes = the opposite of 0, 1, or 2 successes (might be easier to compute)
Oct
29
comment Elementary matrix proof
Do you mean mu times m if i=l and k=m?
Oct
29
comment How to parametrize a curve using polar coordinates
Well, in polar coordinates, x = (what), and y = (what) in terms of r and theta? Figure that out and you're well on your way.
Oct
29
comment Torn between plugging back into the original vs. an intermediate equation…
OK, I think I see what you're asking: if you solve the simpler equation, will all of those solutions still solve the original equation. In this case, they do, but, in general, they might not. In particular, if the simpler equation is itself quadratic (or quartic, etc), the simpler one may give you extraneous roots. So, yes, you need to check that the simpler equations solutions still work with the original equation.
Oct
29
comment Remove sticker on the back of Rudin book
Step 1: post question to stackexchange.com, Step 2: wait for answer in form of a comment. Step 3: wait for comment on comment that's really an answer. Step n: wait for comment generated in step n-1. The number of steps is infinite and each step takes finite time. Thus, you can not remove the sticker from the back of the book. - QED
Oct
29
comment Torn between plugging back into the original vs. an intermediate equation…
I prefer plugging into y=3x-1, because you avoid the "extraneous roots" you'd get by plugging into the original.
Oct
29
comment Understanding Mathematical Symbols in Algorithms
I think it means T(i,j)=0 when j<i. I read it as "for all i and j, when j<i".
Oct
27
comment A question about $f(x)\equiv 0$
Derivative of both sides using product rule and fundamental theorem of calculus for right side? We know g'(x) <= 0 everywhere. That, combined with the fact that a negative times a negative is positive MAY (or may not) help.
Oct
27
comment an example of a sequence $(u_n)_n$ taking its values in $[-1,+1]$ such that $(u_{n+1}-u_n)$ converge to zero but $(u_n)_n$ does not converge
If I understand correctly, you're creating a sub-sequence where u(n) bounces between approximately -1 and approximately 1, and thus never converges, is that correct?
Oct
26
comment Is there a difference in the rate of decrease between $f(x)$ and $g(x)$ for increasing $x$?
That's a subjective question, but I would argue "not really", since both functions are O(1/x).
Oct
19
comment Set of numbers which can not be represent as $a_1^n+a_2^n+…a_n^n$
@Antony Ah, OK, so I did misunderstand your question. The solution you give there is for ai=1, which I should've excluded.