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Laplace's Demon

 Mathematics

Associated with Math.SE; for both general discussion & math qu...
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Brook Taylor
May 14, 2021 13:02
Hello everyone! :)
Brook Taylor
May 7, 2021 21:41
Do you have any idea about path-connectedness?
Brook Taylor
May 7, 2021 21:40
Wait no
Brook Taylor
May 7, 2021 21:40
@leslietownes Yeah! I do
Brook Taylor
May 7, 2021 21:30
Otherwise, I might just go to bed
Brook Taylor
May 7, 2021 21:30
Does anyone have a clue about this?

https://math.stackexchange.com/questions/4131069/types-of-connectedness-for-l-n-x-fracxn-mid0-leq-x-leq1-subset-math
Brook Taylor
May 7, 2021 21:29
Yeah
Brook Taylor
May 7, 2021 21:08
The self-esteem is really low since I goofed up and made a fool of myself a while ago
Brook Taylor
May 7, 2021 21:07
I think I figured out one part of my question
Brook Taylor
May 7, 2021 21:07
Yey
Brook Taylor
May 7, 2021 21:00
Haha, I have no clue about that stuff!
Brook Taylor
May 7, 2021 20:55
Ahh I see
Brook Taylor
May 7, 2021 20:52
Why would a function be constant just because the preimage is clopen?
Brook Taylor
May 7, 2021 20:50
Usually just do programming and now this haha
Brook Taylor
May 7, 2021 20:49
I'll say
Brook Taylor
May 7, 2021 20:47
0
Q: Types of connectedness for $L_n:=\{(x,\frac{x}{n})\mid0\leq x\leq1\}\subset\mathbb{R}^2$ for $n\in\mathbb{Z}_+$

Brook TaylorExercise: Let $L_n:=\{(x,\frac{x}{n})\mid0\leq x\leq1\}\subset\mathbb{R}^2$ for $n\in\mathbb{Z}_+$. Then consider $X=\{(1,0)\}\cup\bigcup_{n=1}^\infty L_n\subset\mathbb{R}^2$ together with the subspace topology. Is this topological space path-connected, connected, and/or locally connected? Explai...

general-topology connectedness path-connected locally-connected
Brook Taylor
May 7, 2021 19:58
Hang in there.
Brook Taylor
May 7, 2021 19:55
Is that algebraic topology that you are discussing?
Brook Taylor
May 7, 2021 19:02
For me, it's this stuff that I need help with: Not getting a lecture or lecture notes. I can watch or read that just fine on my own. I need to fight with some exercises and then get some instruction on how to proceed when I'm stuck.
Brook Taylor
May 7, 2021 19:01
Like a blend of lecture and a problem-solving session?
Brook Taylor
May 7, 2021 18:59
Mustn't it be so boring to lecture the same thing every year for 40 years?
Brook Taylor
May 7, 2021 18:59
Seriously though
Brook Taylor
May 7, 2021 18:59
Haha
Brook Taylor
May 7, 2021 18:57
Sounds more like Voodoo than teaching to me though.
Brook Taylor
May 7, 2021 18:57
The professor should be on the wall.
Brook Taylor
May 7, 2021 18:56
Not that way
Brook Taylor
May 7, 2021 18:56
What do you think about flipped classroom?
Brook Taylor
May 7, 2021 18:55
It's amazing seeing how difficult the students have with any programming, and how they can't tackle problem shooting.
Brook Taylor
May 7, 2021 18:52
At least I did before I started working as a TA at the IT department.
Brook Taylor
May 7, 2021 18:52
As a student you don't get that though. You think it's easy.
Brook Taylor
May 7, 2021 18:51
Being a teacher is infinitely difficult though.
Brook Taylor
May 7, 2021 18:50
:)
Brook Taylor
May 7, 2021 18:50
I'm also sorry I spammed the chat for a while.
Brook Taylor
May 7, 2021 18:49
Thank you!
Brook Taylor
May 7, 2021 18:48
So all of that just because I drew the set wrong. The devil truly is in the details.
Brook Taylor
May 7, 2021 18:46
I owe you an apology, and a big thank you, Ted.
Brook Taylor
May 7, 2021 18:45
Well, I studied since 8 am this morning so...
Brook Taylor
May 7, 2021 18:45
I stared myself blind at the fact that I had drawn it wrong, and that there were two cut-out regions.
Brook Taylor
May 7, 2021 18:44
Yes
Brook Taylor
May 7, 2021 18:44
Sigh...
Brook Taylor
May 7, 2021 18:44
Ohhh...
Brook Taylor
May 7, 2021 18:44
and on top we get $(-1-\epsilon,-1+\epsilon)$
Brook Taylor
May 7, 2021 18:43
So on the left we have $(-1-\epsilon,-1]$
Brook Taylor
May 7, 2021 18:41
Yikes
Brook Taylor
May 7, 2021 18:41
I drew it like the closed set was open and the open one closed.
Brook Taylor
May 7, 2021 18:41
I drew it as the set which we remove looks
Brook Taylor
May 7, 2021 18:41
I drew it wrong
Brook Taylor
May 7, 2021 18:41
Damn
Brook Taylor
May 7, 2021 18:41
Yeah
Brook Taylor
May 7, 2021 18:40
It's not removed from $\mathbb{R}^2$ as the set $(-1,1)\times(-2,2)$ is open