« first day (2161 days earlier)      last day (2771 days later) » 
00:00 - 03:0003:00 - 04:0004:00 - 05:0005:00 - 13:0013:00 - 18:0018:00 - 19:0019:00 - 22:0022:00 - 00:00

0celo7
0celo7
10:04 PM
no
$g(x,y)=\frac{x^2y}{x^2+y^2}$ at $(x,y)\ne (0,0)$ and $=0$ at $(x,y)=(0,0)$
how do show this is continuous at $(0,0)$?
 
user218912
just do an epsilon-delta thing
 
0celo7
0celo7
how?
 
Slereah
Slereah
Or use the continuity of hyperreal functions, obviously
 
0celo7
0celo7
what?
 
Slereah
Slereah
$f(0,0) \approx f(\varepsilon, \varepsilon)$
 
0celo7
0celo7
10:07 PM
...what?
 
Slereah
Slereah
Since $f(\varepsilon, \varepsilon) = \frac{\varepsilon^3}{2\varepsilon^2} = \frac{\varepsilon}{2}$ it is obviously continuous
 
user218912
seems reasonable but idk what hyperreal functions are.
 
Slereah
Slereah
I am just being facetious
Because that is not calc 3
 
user218912
is it legit though?
 
Slereah
Slereah
yes
 
0celo7
0celo7
10:12 PM
i highly doubt it
 
Slereah
Slereah
Doing with deltas and epsilons is pretty tedious because it has two variables
Though at least it's at 0
It's like
 
user218912
you will need some identities I think.
 
Slereah
Slereah
$|x| < \delta_x, |y| < \delta_y$
Oh wait, right, I can't even do both at once
Since otherwise that would divide by 0
You gotta prove step by step continuity at (0,y) and (x,0)
pretty tedious
 
0celo7
0celo7
no you have to prove continuity along every curve if you want to do it that way
 
Slereah
Slereah
sounds even worse
 
0celo7
0celo7
10:15 PM
that's p. hard
 
user218912
I'm bad at non-obvious things.
 
user218912
[I'm also bad at obvious things it seems]
 
user218912
but much better than non-obvious.
 
Slereah
Slereah
There's a few examples here
Pretty similar looking
 
user218912
@0celo7 what colour is your ipad?
 
0celo7
0celo7
10:20 PM
space gray
@Slereah I know how to show a limit doesn't exist
but it's very hard to show one does exist
 
user218912
@0celo7 idk if I should get silver or space gray.
 
0celo7
0celo7
Ok, so what I need is:
$(\forall\epsilon>0)(\exists \delta>0): (x,y)\in B_\delta(0,0)\implies$ $$\left|\frac{x^2y}{x^2+y^2}\right|<\epsilon$$
fug
PhD level calculus...
 
user218912
more like freshman calculus.
 
0celo7
0celo7
you can't do it
 
user218912
exactly.
 
0celo7
0celo7
10:25 PM
???
 
Slereah
Slereah
If $(x,y)$ is in the ball of radius $\delta$ then $(x,y) < (\delta, \delta)$
 
0celo7
0celo7
Wait.
I think I have it.
$$\frac{x^2y}{x^2+y^2}\le \frac{x^2y}{x^2}=y\to 0$$
is that correct?
 
Slereah
Slereah
Yes
 
0celo7
0celo7
I think so because $y^2$ is positive
ok so it's trivial
good
squeeze theorem!
I should organize my books
@IceLord I'm wondering what color my new phone should be
 
user218912
@0celo7 what colour is it now?
 
0celo7
0celo7
10:32 PM
space gray
ok time to find a mathematical avatar
 
user218912
I would go with silver.
 
0celo7
0celo7
Figures.
 
user218912
what?
 
user218912
only because every device I have owned is always black.
 
0celo7
0celo7
what's a good mathy picture
 
user218912
10:34 PM
I'm bored of it.
 
user218912
so I would try white for a change.
 
user218912
@0celo7 the one I linked yesterday.
 
user218912
the second one.
 
0celo7
0celo7
I don't remember thinking it was good
 
user218912
 
0celo7
0celo7
10:35 PM
what the hell is that
 
user218912
lol
 
user218912
it's some manifold
 
0celo7
0celo7
doesn't look like one
 
user218912
idk well I searched up "blue manifold"
 
user218912
what about a lorenz attractor?
 
user218912
10:40 PM
 
0celo7
0celo7
I don't know anything about those
 
user218912
 
0celo7
0celo7
there are some good pictures in HE
yeah I definitely don't want algebraic geometry
aha
I know
 
user218912
 
0celo7
0celo7
what the hell
 
Slereah
Slereah
10:44 PM
That is a spooky skeleton
 
0celo7
0celo7
I need to do PhD photoshop
 
user218912
to do what?
 
0celo7
0celo7
dammit it got partially cut off
 
user218912
omg I remember that image.
 
user218912
it was in a book I read.
 
user218912
10:48 PM
don't remember which book.
 
0celo7
0celo7
Arnold
you did not read Arnold, I gurantee
 
user218912
I read parts of it.
 
user218912
remember?
 
0celo7
0celo7
no
I don't think you do either
I need a square image
 
user218912
I do... wtf.
 
0celo7
0celo7
10:49 PM
hence PhD photoshop
 
user218912
okay upload the image here and I'll fix it for you
 
user218912
unless you know PhD photoshop
 
0celo7
0celo7
no I do not
 
Slereah
Slereah
 
user218912
@0celo7
 
user218912
10:55 PM
 
user218912
or I prefer you use this
 
user218912
 
user218912
just sayin
 
0celo7
0celo7
...dude
 
user218912
do you want me to remove the text btw?
 
0celo7
0celo7
10:57 PM
oh sure
that would be great
 
user218912
blue or white?
 
0celo7
0celo7
white
 
user218912
:(
 
user218912
k
 
user218912
oh my bad
 
0celo7
0celo7
10:59 PM
?
 
user218912
the text still shows
 
user218912
a tiny bit
 
user218912
 
user218912
@0celo7
 
user218912
the blue one looks better tbh
 
0celo7
0celo7
11:04 PM
very good thanks
 
user218912
np
 
user218912
brb food
 
user218912
11:27 PM
It says I got 0 on the last 3 problem sets for freshman physics class even though I handed in excellent solutions on time?
 
user218912
I will have to discuss this with the prof.
 
0celo7
0celo7
tes
hmm
my avatar is screwed up
@IceLord rekt
 
user218912
what do you mean?
 
0celo7
0celo7
 
user218912
@0celo7 no, more like I probably put it in the wrong dropbox.
 
user218912
11:31 PM
@0celo7 it's fine for me.
 
user218912
reload the page...
 
0celo7
0celo7
I did
wtf it worked that time
 
user218912
okay time to read ahead in qft.
 
0celo7
0celo7
ask questions I need Lee
I need to learn manifolds
 
user218912
I'll buy it for your birthday.
 
0celo7
0celo7
11:53 PM
do you want my paperback lol
I might give it to my advisor if not
or are you done with math?
 
00:00 - 03:0003:00 - 04:0004:00 - 05:0005:00 - 13:0013:00 - 18:0018:00 - 19:0019:00 - 22:0022:00 - 00:00

« first day (2161 days earlier)      last day (2771 days later) »