Reputation
1,779
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
9 29
Newest
 Announcer
Impact
~64k people reached

Feb
6
awarded  Announcer
Jan
25
comment Prove that greatest common divisor of two numbers multiplied with itself divides the product of those numbers
@user236182 well, the only way $p$ and $q$ would not be distinct is if $a=b$, in which case by definition $c=a=b$ so $p=q=1$... but like you said, that doesn't affect the validity of the proof. Of course one could argue it's important to at least consider corner cases like this.
Jan
19
comment Derivative by definition
@YvesDaoust are you suggesting CodeNinja mark the changed part of the question with "EDIT:" or the like? I thought the recommended practice on SE sites was not to do that. Though I suppose I don't know if this site has its own particular conventions on the topic.
Jan
14
comment Why is the derivative at an instantaneous point, but the integral is the area of the whole function?
I think this is a pure math question and thus off topic here. If other people agree, we can migrate it to Mathematics.
Jan
8
comment Why is it unacceptable to say “the range is a function of the domain”?
@CarlLeth Yeah, I think it would make more sense to have the domain be how you hit the balls, rather than the balls themselves. But you could define a "subfunction" whose domain is the ways in which you actually did hit one of the balls (rather than all the possible ways you could hit a ball), and in that case the range would be the locations where balls actually landed.
Jan
3
comment How to get the complex number out of the polar form
@MaskedMan Current never appears in an exponent. On top of that, we typically use capital $I$ for current, and/or write it as a function of time, $I(t)$ or $i(t)$. Throughout all of this, the imaginary unit is always $i$.
Jan
3
comment How to get the complex number out of the polar form
$j^2 = -1$ was engineering notation, I thought. I'm a physicist and I've never used it nor seen anyone in my field use it. We've all standardized on $i$ for the imaginary unit (and $j$ has no special meaning with regard to complex numbers).
Dec
31
comment 3 balls into 3 cells problem
That way of thinking applies when you can't put two balls in the same spot (or same position in a line, or so on). It's not about having 3 balls, then 2, then 1; it's about having 3 places, then 2, then 1. That's when the numbers go down each time. If you can reuse places, then you keep multiplying by the same number. 3 times 3 times 3.
Dec
25
comment Check if a Function is Differentiable at a Point
@gbox A clarification might help us: if you were to take $h$ to the desired point (for example, to test differentiability at $3$, taking $h\to 3$), what do you think $x$ would be?
Dec
22
comment A valid floor function trick?
Does this handle the (hypothetical) case where $\left\lfloor\frac{\left\lfloor\frac{x}{m}\right\rfloor}{n}\right\rfloor$ and $\left\lfloor\frac{x}{mn}\right\rfloor$ are consecutive integers, so there is no $N$ between them? For instance, if $\frac{x}{mn} = N = \left\lfloor\frac{\left\lfloor\frac{x}{m}\right\rfloor}{n}\right\rfloor - 1$?
Dec
8
comment Math induction problem with large numbers
A good proof (or demonstration, if one wants to be picky), but not an inductive one as the question required. However I do think this is good motivation for the step that is missing in several of the other answers, which is why one should try to prove $10 \vert (17^{4n} - 1)$ in the first place.
Dec
6
comment Convincing Myself of Stamp Induction Induction Proof?
I think it was this answer that suggested thinking of induction not as building up from one case of a problem to the next, but breaking down a given case into simpler cases of the same problem. I think that might be useful here for the $n+3$ induction. Given this problem for any $n>14$, you can reduce it to the same problem with $n-3$, and then $n-6$, etc., and you will eventually run into one of the proven base cases 12, 13, or 14. That's equivalent to the induction argument, just in the other direction.
Dec
4
comment Can we always multiply some function that is not differentiable everywhere with function that is to obtain differentiable product?
This seems to imply that given any $f$ (whether nowhere differentiable or differentiable at some points), if there exists a $g$ such that $f$ is not differentiable at $x$ but $fg$ is, then $g(x)=0$. Or am I missing something? I think that's a decently interesting result in its own right.
Nov
21
comment What is exactly meant by “preserves the group operation”?
@GniruT what Michael described in his answer is practically the definition of preserving an operation. Maybe you could clarify what about this still confuses you?
Nov
11
comment What's the right way to make a change of variables under another integral?
@Hans the source is arxiv:1203.6139, equation (45).
Nov
11
comment Why would the eigenvalues of this type of (stochastic) matrix all be close to 1?
Actually, to be fair, it answers the first part of my question. (Though user1551's answer does the same.) What I'm really interested in is the second part.
Nov
11
comment Why would the eigenvalues of this type of (stochastic) matrix all be close to 1?
I'm not claiming that all eigenvalues of $T$ are 1. It's an empirical observation that they tend to be close to 1, so unless you're saying there is a programming error in the linear algebra library I use, it does no good to suggest a computational error. This is good information to have, sure, but it doesn't answer my question.
Nov
9
accepted Symbolically solving coupled partial differential equations
Nov
9
comment Symbolically solving coupled partial differential equations
I think that should do it. If something goes wrong applying this to my real case (which is a bit more complicated), I'll post a followup question.
Nov
8
asked Symbolically solving coupled partial differential equations