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leslie townes
leslie townes
00:11
i generally assume that everyone in australia is within a few feet of some wild animal or insect that could kill them at all times.
LearningCHelpMeV2
LearningCHelpMeV2
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(i). I eventually solved this problem by considering different ranges of values. But I would like to know why my initial approach doesn't work?
I did the following
$\deg(p(x))=m \iff \deg(p^3(x))=m^3$

So $p^3(x) -3p(x)=-2x \iff m^3-m=1$
leslie townes
leslie townes
where does m^3 - m come from? degree is not additive.
for example the degree of x^8 - 3x^2 is 8, not 8 - 2.
looking at degrees is definitely a solid approach, but not quite like that.
LearningCHelpMeV2
LearningCHelpMeV2
oh wow
yeah sorry
thanks
Ted Shifrin
Ted Shifrin
Creativity can be interesting!
 
13 hours later…
monoidaltransform
monoidaltransform
13:41
Let $H^1_{0}(U)$ be the closure of the test functions in the $W^{1,2}(U)$ sobolev spaces.
Is $H^{1}_{0}(U)$ just the space of test functions?
in other words is the space of test functions closed wrt to the $W^{1,2}(U)$ norm?
monoidaltransform
monoidaltransform
13:52
because thought I understand that the weak derivatives of functions in $H^1_0(U)$ exist
I don't see why classical derivatives should exist
 
4 hours later…
Ted Shifrin
Ted Shifrin
17:29
@monoidal Didn’t you just answer your question? Can’t a function with only weak derivative be a limit of functions with actual detivatives?
Ted Shifrin
Ted Shifrin
18:10
checks pulse of the room and finds none
leslie townes
leslie townes
beep. beep. beeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Ted Shifrin
Ted Shifrin
Maybe Munchkin can perform the autopsy.
leslie townes
leslie townes
i don't know what to make of this. last week the theory was that everybody was partying at your house.
robjohn
robjohn
18:31
@leslietownes it was quiet for 13 hours last night.
leslie townes
leslie townes
well, that was the party at my house.
robjohn
robjohn
18:53
@leslietownes so is next week at copper top's?
Ted Shifrin
Ted Shifrin
Geographically speaking, no, it’s at your place, @robjohn!
robjohn
robjohn
My wife will be so pleased.
Ted Shifrin
Ted Shifrin
We promise to bring our own martinis.
robjohn
robjohn
good, the alcohol supply here is limited mainly to wine.
Ted Shifrin
Ted Shifrin
@leslie will bring the agridolce leeks with pine nuts.
copper.hat
copper.hat
19:43
wine is good
Ted Shifrin
Ted Shifrin
20:12
whines
 
2 hours later…
forest
forest
21:48
Very simple question, but is there any difference between [0,n] and [0,n) when specifying an interval from 0 to n?
Ted Shifrin
Ted Shifrin
@forest The latter does not include $n$, of course.
forest
forest
@TedShifrin Ah, so [0,n-1] is the same as [0,n)?
math.net/interval-notation OK, I get it.
You can tell I'm quite new to this lol
Ted Shifrin
Ted Shifrin
If our world is just integers, yes.
forest
forest
22:03
Just integers, yes.
gf.c
gf.c
hi all, is there a natural isomorphism $\text{End}(V)^* \cong \text{End}(V^*)$ where $V$ is a finite-dimensional vector space?
Ted Shifrin
Ted Shifrin
22:23
So this is asking if $(V^*\otimes V)^*$ is naturally isomorphic to $V\otimes V^*$.
So we need $(V\otimes W)^* \cong V^*\otimes W^*$ and $V^{**} \cong V$.
Seems natural enough to me (the latter one uses finite-dimensionality to make sure an injection is bijective).
gf.c
gf.c
perfect! thanks so much, very clear
Ted Shifrin
Ted Shifrin
Oh, I already used $V^{} \cong V$ in my reduction. I should have had $V^{}\otimes V^* \cong V\otimes V^*$ as the second space.
What in the world is going on with MathJax?
Let me try again. Maybe there's a hidden bad symbol somewhere.
I give up.
Ted Shifrin
Ted Shifrin
22:51
$V^{**}\cong V$
Working fine now. I have no clue. I rebooted my desktop just for good measure.
Wow. This got scarier and scarier.
leslie townes
leslie townes
23:07
eek, yeah.
Ted Shifrin
Ted Shifrin
I got a little snide.
Wojciech Kulma
Wojciech Kulma
23:45
why does this hold? https://math.stackexchange.com/a/2811127/625288

I'm trying to use the borell-cantilli but it doesn't bring me anywhere near the result

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