The h Bar

« first day (2161 days earlier) ← previous day next day → last day (3063 days later) »

0celo7

22:04

$g(x,y)=\frac{x^2y}{x^2+y^2}$ 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

how?

Slereah

Or use the continuity of hyperreal functions, obviously

0celo7

what?

Slereah

$f(0,0) \approx f(\varepsilon, \varepsilon)$

0celo7

22:07

...what?

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

I am just being facetious

Because that is not calc 3

user218912

is it legit though?

Slereah

yes

0celo7

22:12

i highly doubt it

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

$|x| < \delta_x, |y| < \delta_y$

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

no you have to prove continuity along every curve if you want to do it that way

Slereah

sounds even worse

0celo7

22:15

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

tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx

There's a few examples here

Pretty similar looking

user218912

@0celo7 what colour is your ipad?

0celo7

22:20

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

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

you can't do it

user218912

exactly.

0celo7

22:25

???

Slereah

If $(x,y)$ is in the ball of radius $\delta$ then $(x,y) < (\delta, \delta)$

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

Yes

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

22:32

space gray

ok time to find a mathematical avatar

user218912

I would go with silver.

0celo7

Figures.

user218912

what?

user218912

only because every device I have owned is always black.

0celo7

what's a good mathy picture

user218912

22:34

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

I don't remember thinking it was good

user218912

this?

0celo7

22:35

what the hell is that

user218912

lol

user218912

it's some manifold

0celo7

doesn't look like one

user218912

idk well I searched up "blue manifold"

user218912

what about a lorenz attractor?

user218912

22:40

this?

0celo7

I don't know anything about those

user218912

k3 surface

0celo7

there are some good pictures in HE

yeah I definitely don't want algebraic geometry

aha

I know

user218912

0celo7

what the hell

Slereah

22:44

That is a spooky skeleton

0celo7

I need to do PhD photoshop

user218912

to do what?

0celo7

dammit it got partially cut off

user218912

omg I remember that image.

user218912

it was in a book I read.

user218912

22:48

don't remember which book.

0celo7

Arnold

you did not read Arnold, I gurantee

user218912

I read parts of it.

user218912

remember?

0celo7

I don't think you do either

I need a square image

user218912

I do... wtf.

0celo7

22:49

hence PhD photoshop

user218912

okay upload the image here and I'll fix it for you

user218912

unless you know PhD photoshop

0celo7

no I do not

Slereah

user218912

@0celo7

user218912

22:55

user218912

or I prefer you use this

user218912

just sayin

0celo7

...dude

user218912

do you want me to remove the text btw?

0celo7

22:57

oh sure

that would be great

user218912

blue or white?

0celo7

white

user218912

oh my bad

0celo7

22:59

user218912

the text still shows

user218912

a tiny bit

user218912

@0celo7

user218912

the blue one looks better tbh

0celo7

23:04

very good thanks

user218912

brb food

user218912

23:27

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

tes

hmm

my avatar is screwed up

@IceLord rekt

user218912

what do you mean?

0celo7

user218912

@0celo7 no, more like I probably put it in the wrong dropbox.

user218912

23:31

@0celo7 it's fine for me.

user218912

reload the page...

0celo7

I did

wtf it worked that time

user218912

okay time to read ahead in qft.

0celo7

ask questions I need Lee

I need to learn manifolds

user218912

I'll buy it for your birthday.

0celo7

23:53

do you want my paperback lol

I might give it to my advisor if not

or are you done with math?

« first day (2161 days earlier) ← previous day next day → last day (3063 days later) »

all rooms

Transcript for

Oct3

Oct '164

Oct5

General chat for Physics SE (physics.stackexchange.com). For M...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC