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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


Apr
12
comment Best and most efficient way to numerically compute $e$?
@Martin has hit the nail on the head. Your last error term is on the order of machine epsilon for double-precision floating-point. If you check the values between 10 and 100, you should find that the error stops decreasing because the successive terms are too small to be represented in the usual double data type.
Apr
12
comment How do I solve this differential equation?
Then what's the problem?
Apr
12
answered Connecting all points on a plane with shortest path possible
Apr
12
comment Improving my understanding of Cantor's Diagonal Argument
They're not integers, either. They're just infinite sequences of digits.
Apr
12
comment How do I solve this differential equation?
Can you include in the question what you get when you substitute $\Phi=f(\gamma)/\gamma$?
Apr
12
answered Improving my understanding of Cantor's Diagonal Argument
Apr
12
comment Improving my understanding of Cantor's Diagonal Argument
For your last sentence, see Why Doesn't Cantor's Diagonal Argument Also Apply to Natural Numbers?
Apr
12
comment What are examples of legitimate usage of logarithmic scale when drawing a chart?
I feel that the abuse there lies more in misrepresenting the scale of the graph rather than in the use of a log scale itself.
Apr
12
comment What are examples of legitimate usage of logarithmic scale when drawing a chart?
What do you consider an illegitimate case or abuse of the logarithmic scale? Certainly if one is visualizing a power law or exponential growth/decay then a [semi-]logarithmic scale makes it easier to see.
Apr
12
comment $A, B$ sparse imply $AB$ is sparse?
@Nick: yes, I added an example showing that the product can be quite dense.
Apr
12
revised $A, B$ sparse imply $AB$ is sparse?
added 538 characters in body
Apr
12
comment Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?
@anon +1 That was hilarious and unexpected. That said, if I see more than one meme post a day on this site, I'm flagging 'em.
Apr
11
revised What I'm doing wrong with this demonstration trigonometric?
formatting
Apr
11
comment Normal distribution (why $\Phi(0,1)=0.5\Phi(-1,1)$)
I don't know, check your book. But how does it matter?
Apr
11
comment Normal distribution (why $\Phi(0,1)=0.5\Phi(-1,1)$)
Oops, I meant $\Phi(-1,1) = \Phi(-1,0) + \Phi(0,1) = 2\Phi(0,1)$, with a plus sign. You know that $\Phi(a,b) + \Phi(b,c) = \Phi(a,c)$, right?
Apr
11
comment Trying to solve for X. Memory fails me.
It's better to introduce symbols and abbreviations the first time you use them. In particular, I would say "we can define an action of the special linear group $\mathrm{SL}(2)$" and similarly for $\mathrm{GL}(2)$. That way, even if someone doesn't have the background for what you're saying, they know how to look it up if they want.
Apr
11
comment Normal distribution (why $\Phi(0,1)=0.5\Phi(-1,1)$)
If $\Phi(a,b)$ is the probability that a standard normal random variable lies between $a$ and $b$, then this follows from the fact that the normal distribution is symmetric about its mean, in this case zero. So $\Phi(-1,0) = \Phi(0,1)$ and $\Phi(-1,1) = \Phi(-1,0) - \Phi(0,1) = 2\Phi(0,1)$.
Apr
11
comment When is this equation true?
The answer is: when the function $h$ is continuous at $(l_1,l_2)$.
Apr
11
comment Are these two statements equivalent?
Oh, and I almost forgot: -1 for calling me an abnormal human being!
Apr
11
comment Length of the zero level set of a function
Christian's answer is nice. I just want to point out that the paper by Zhao et al. does cite an reference which is said to contain the proof.