at UGA some of the grad students told grad students never to take a class from me because I was too demanding ... well, do you want to learn something or not?
(In fairness, I think they admitted I was a good lecturer/teacher, but ...)
We call that the binomial theorem, @Lucas. But I have no idea why you can't have cancelling terms.
Demonark, you're doing fine, aside from our little spats. Of course it's uphill. And it will get steeper. But if you're passionate and truly want it ... go for it.
It's more like, I dunno, there's some resistance on the family side since I think most of an academic career as being a minimal upgrade of a high school teacher, and that the hell required to get this far would have just been thrown down the drain. So it'll take some time to get everyone to realize that it's actually different
Yeah I mean, I definitely want to at least attempt grad school, I think the concern is more, after that. Which can wait but you know, they're from Morocco, whose education system is modeled after Europe
But do think about contingencies, because academia is becoming a harder road with the current views in the US (and I'm not meaning just the idiot president).
@Lucas: Honestly, I haven't tried to do it. I might know some algebra you don't that I might try to use (and I'd let $a,b\in\Bbb Q$ to apply that). But I don't know a proof yet. You might need to learn up through chapter 7 stuff in my book, though :P
I think what Semiclassic said is worth thinking about seriously. Get some computer skills. Investigate biomath/bioengineering (which is super-hot still). Whatever.
"It" referring to the situation and not to the baby
@Daminark I while ago I learned that there was a star such that the relative size of the Earth to this star was the same as the relative size of a second to two days
which kinda broke my mind because while obviously I have an intuitive understanding of a second and of a two-day duration, I don't know if I feel them on the same scale
@Semiclassical Distance to Alpha Centauri is almost exactly a century IIRC
Hm. Imagine it were possible to send a radio wave out into space in such a way that, when it came into contact with whatever planet we were aiming at, it would assemble the nearby atoms into a clone of you
which I'm sure is impossible for a variety of reasons
Hi -- can someone kindly shed any light for this Q: https://math.stackexchange.com/questions/2376054/satisfying-the-following-determinant-inequality thank you!
Can anyone shed some light on interpretation of a conservation law for me? If I have a conservation law C = stuffhere and I move to a different jet space (in different space of variables) what is the significance of C = 0 = stuff here in the new jet space?
Hm. Imagine it were possible to send a radio wave out into space in such a way that, when it came into contact with whatever planet we were aiming at, it would assemble the nearby atoms into a clone of you
Even if the radio wave is 100% efficient, and not deflected nor degraded as it pass through interstellar dust, without the knowledge of the atomic composition and distribution at the destination, it is impossible to program the wave in a way such that it can induce assembly of atoms into a clone
Hi. I'm aware that (x+y)^2 = x^2 + 2xy + y^2 and also that you can use Pascal's Triangle and the Binomial Expansion to find (x+y)^n with its factors. I'm trying to confirm whether the same is true when using subtractions, i.e. (x-y)^n ?
Thanks in advance!
To clarify, I'm not asking if (x-y)^2 = x^2 + 2xy + y^2; I know it's x^2 - 2xy + y^2; I'm asking if the same logic can be used and if there's a pattern for the + and - signs in the factors retrieved from Pascal's Triangle.
@Semiclassical That makes sense. I was seeing it as x+(-y), but had not tried expanding larger powers and wasn't 100% sure what the + and - pattern would be. Thanks.
Are there nonconstant solutions $U,V,W$ such that for all real $x,y$ we have
$$ U(x+y) = U(x) V(y) W(y) + U(y) V(x) W(y) + U(y) V(y) W(x) + U(y) V(x) W(x) + U(x) V(y) W(x) + U(x) V(x) W(y) $$
How to decide existance or uniqueness ?
Can we express the solutions with closed forms or differential...
@mick what are the standard functions? Be specific. Otherwise, someone will answer your question and you'll just say "no, because it isn't a closed form solution"
@skullpatrol I choked on the lack of math skills here.
@mick For all I know, that is an unsolved conjecture. Way outside of my league.
Elementary , trig , exp , log , theta , hypergeo , ei li si Bessel gamma beta zeta Lambertw clausen polylog Mathieu , the compositions and inverses , those are standard functions
@mick Fair enough. Just recommending an edit so people don't get confused later. Ummm... I have no clue man. I can only throw guesses and test them. I have no experience with that. I presume piecewise constant works but that's just a guess considering constant works.
@skullpatrol I believe an inductive proof can be done for elements of the forms 12n + 3 and 12n + 7. It's just a matter of splitting the cases in just the right way. It might be that it only works if you consider things like 1024q + r.
@Semiclassical how can it not be resolvable? If it is false, we eventually find a counter-example. If it is true, then there exists a proof such that it can be shown true.
Let $r(a,b)$ be a rational number depending on $a,b$ and nonnegative. For every $b$ there is an $a$ such that $r(a,b)$ is not $0$.
Let $C(a,b)$ be a squarefree positive integer depending on $b$ and different for every $b$.
Consider for positive integers $I,J$ :
$$ S_J = \sum_{j=1}^J \sum_{i=1}...
Are there nonconstant solutions $U,V,W$ such that for all real $x,y$ we have
$$ U(x+y) = U(x) V(y) W(y) + U(y) V(x) W(y) + U(y) V(y) W(x) + U(y) V(x) W(x) + U(x) V(y) W(x) + U(x) V(x) W(y) $$
How to decide existance or uniqueness ?
Can we express the solutions with closed forms or differential...
