12:02 AM
@Josh If M/L/K is a tower of Galois extensions, then Gal(L/K)->Gal(M/K)->Gal(M/L) is a pair of group homomorphisms. the first is one-to-one, the second is onto, and the image of the first is precisely the kernel of the second. when we have H->G->K (for some groups H,G,K) with those properties, we cannot say that G is a direct product of H and K (not even a semidirect product in general).
@evinda Make Y the subspace of sequences that are eventually bounded by r^n for some r<1, and make x(n)=1/n.
or you could make Y the subspace of sequences that are just 0s with finitely many exceptions, and make x any sequence with infinitely many positive terms

Can someone help me with a quadratics question

12:24 AM
what is it

3 hours later…
3:46 AM
it sure is a good feeling to finally finish all the assignments you have due in a really busy week

2 hours later…
5:31 AM
I have a map of spaces $f_t: X \to F_t$. The $F_t$ are all noncanonically isomorphic, and putting this together for all $t$, I obtain a map $X \times [0,1] \to F$, where $F$ fibers over $[0,1]$ with fiber $F_t$. This is an uncomfortable situation; I'd like the codomain to have dimension one lower. I have fiddled for a bit but can't see how to reduce the dimension of the codomain without just trivializing the bundle and projecting (which I would like not to do). Thoughts?
Would prefer something more natural/functorial, whatever that means. If you'd like, pretend everything here is a smooth map of smooth manifolds.

1 hour later…
6:59 AM
@robjohn How was the turkey?

@JasperLoy It was very nice. How was your day?

@robjohn I slept through most of it. I think about things, get tired, and then sleep.
It's almost time for SE hats again.

What textbook should I learn calculus from, from a rigorous viewpoint, given that I have already done much more 'advanced' mathematics?

7:46 AM
@MikeMiller Does "huh?" count as a thought?

4 hours later…
11:16 AM
Why is $\sqrt{n} = n^{\frac{1}{2}}$ ?

@OverlyExcessive $\sqrt{a}^2=a=a^{\frac12 \times 2}$
I am new here, so I am not sure if it is normal that we have pretty much no chat here?

@I'mmostlyjustanidiot It varies a lot

11:31 AM
@TobiasKildetoft As in on a day to day basis, or there are what part of the year that we are in trends?

@I'mmostlyjustanidiot Not sure

Can you elaborate on this please I am not 100% sure, $a^{\frac{1}{2}} \ne a^{\frac{1}{2} * 2}$

Try \ne for 'not equal'
No you missed my $\sqrt{2}^{\huge 2}$

So we pick $Y=\{ x \in l^2(\mathbb{N}): \sum_{j=1}^{\infty} |x_j|^2< r^n \text{ for some } r<1 \}$ and $x(n)=\frac{1}{n}$, right?
But how can we now find the distance $||x-Y||= \inf \{ ||x-y||: y \in Y\}$ ?

@robjohn
Yesterday i answerd this question http://math.stackexchange.com/questions/1547804/cauchys-theorem-prove-that-sum-n-1-infty-frac1-lambda-n2-f/1547878#1547878 and get a request how to justify the contour of integration i used. I did think about this a little while but don't get to a rigorous justification which goes beyond "because it works". Because i think u are an expert on this kind of calculations , i kindly ask you if you could give me a hint in the right direction.

11:45 AM
@I'mmostlyjustanidiot Yes, on weekends on holidays.