@Cryin yeah, the idea is that you know by continuity that the rank doesn't decrease, but the way you know the rank doesn't increase is that it's already capped out
Hmm..., suppose we take the set of reals and remove a countable dense set, is it possible to shift the remaining elements in an order preserving manner so that all the holes are filled in?
Hmm, would we want some sort of thing where the derivative of $\phi_n * u$ is gonna be $\phi_{n-1}*u$? Not sure if that's feasible but if so, I think that might be a worthwhile wishlist?
Or maybe not exactly that but sorta one where it'd be of the same form
It'd be a convolution with a similar kernel so that it still converges uniformly
So we've got that, we've got the exercise where he says to find a book on homological algebra and do every single problem (I want to see a professor assign that)
Quick notation question (I have to ask because google isn't terribly helpful when you try and describe notation). Is my interpretation of the provided picture correct, in that, for jr to be assigned to the first item in the bracket stack, vr must be zero andmvr dot t_hat <= js or is it an or operation?
or am I just plain lost (gotta cover all the cases here)?
the problem is in the context, that math is making non sense, so I, to check everything, I'm going to make sure my assumptions about the notation are correct. That bit came into doubt because it was really weird that it was -jst for any case when the velocity is not 0
I don't follow your logic @Faust. You're saying that it is and. So we must have that $v_r = 0$ and $mv_r \cdot t \leq j_s$... But then $mv_r \cdot t = 0$ so one could just substitute $0 \leq j_s$
no it seems to makes sense in context @GiantCowFilms there are two diffrent coefficients of friction when the friction force is not great enough to make the velocity 0 the $f_f $ is $-j_d \vec{t}$
because if there is any velocity, regardless of whether or not, the static friction force is suffcient to negate it, it defaults to dynamic friction, hence the issue.
the only thing i can think of is that the velocity $v_r$ is somehow pointed in a non tangential fashion to the surface like only of a portion of the velocity is resisting the friction the rest is pushing against the surface
Turns out that the office never had a shredder due to noise concerns and we seldom have work documents that demand such treatment.
But one day the unexpected happened, and we had to literally burn the stuff up in the toilet (with care, of course).
How do others deal with such a situation?
@LeakyNun I think I should have stated the question a bit more precisely. I wanted to mean: "Let $(X,\tau)$ be an ordered topological space. Let $r\in X$. Then is it true that every continuous function $f:[-\infty,r]\to\{\pm 1\}$ is constant?"
can you give an example of a set X and a collection of subsets of X, T , which is not a topology on X, but satisfies the first two conditions for a topology and the third, for all countable index sets I.
basicallys it fails for an uncountable union but is fine with a countable union
@ACuriousMind I was talking to some old friends on irc and they said that I should be ashamed of myself to have written something so offensive and that they were disgusted with my "racist attitudes". Once again, I apologize if I offended anyone on here.
@LeakyNun but then I am comparing the equal I am just checking if the numbers form a parallelogram and not a rectangle. I want to know if there are other things that I need to check for the given 4 numbers such that it is confirmed to be a rectangle?
Turns out that the office never had a shredder due to noise concerns and we seldom have work documents that demand such treatment.
But one day the unexpected happened, and we had to literally burn the stuff up in the toilet (with care, of course).
How do others deal with such a situation?
