Mathematics - 2014-05-11 (page 4 of 4)

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Daniel Fischer

22:00

And whom?

Pedro Tamaroff

The inequality is false.

Ted Shifrin

Oh?

Mike Miller

@Ted Want to help me with an English problem?

Ted Shifrin

Not right at the moment, @Mike. We're embroiled in the analysis problem.

Mike Miller

What if I say it's a linear algebra problem?

Ted Shifrin

22:02

Ah, when $x$ is near $1$, it seems that $$\frac{1+x^{n+1}}{1+x^n}>\root n\of x$$ fails.

So how did you determine it fails, @Pedro?

Pedro Tamaroff

@TedShifrin I used a CAS.

Ted Shifrin

mr eyeglasses would call you a cheater :P

Pedro Tamaroff

But it seems not to happen in a nbhd of $x_n$.

Ted Shifrin

Well, my thinking is that you're wrong.

Although I need use a preliminary inequality which perhaps cost me too much.

Pedro Tamaroff

I want to plot g_n-g_{n+1}

for a nbhd of x_n

How do I do that in Mathematica?

Ted Shifrin

22:05

I just did the plot in Mathematica, @Pedro. Your inequality fails miserably. Manipulate[
Plot[(1 + x^(n + 1))^(n + 1) - x (1 + x^n)^n, {x, 0, 1}], {n, 10,
100}]

While @Pedro's thinking, what's your question, @Mike?

Pedro Tamaroff

@TedShifrin I think it can be salvaged!

`g[k_] := x^k/(1 + x^k)^k - x^(k + 1)/(1 + x^(k + 1))^(k + 1);
Manipulate[
Plot[g[k], {x, 1/((2 k)^(1/(2 k))) - 1/k,
1/((2 k)^(1/(2 k))) + 1/k}], {k, 10, 1000}]`

Plot that.

Ted Shifrin

That's what all the false posters kept saying :P

Pedro Tamaroff

That seems to suggest g_{k+1}>g_k

In a nbhd of x_{2k}-

Ted Shifrin

I removed the $x^k$ factor ...

Mike Miller

@Ted Lay is not my favorite author so it's hard to tell what he means in some problems. I finally translated what he meant.

Pedro Tamaroff

22:12

Well you're smarter than me.

Mike Miller

So no worries.

(not my favorite was changed from some harsher wording)

Pedro Tamaroff

Still I'm screwed. SIGH.

I think.

Ted Shifrin

I think it dips below 0, @Pedro. I'm about to find out.

Pedro Tamaroff

Also all the TeXed up equations should have had x_2n

Mike Miller

Question (not hostile, just curious); why is this problem so interesting?

Ted Shifrin

22:15

I dunno, @Pedro. It doesn't want to show me negative.

Well, I found it interesting, as I enjoy uniform convergence arguments and couldn't find one that worked. And then a dozen people keep getting it wrong. So that makes it more intriguing.

Pedro Tamaroff

@MikeMiller Cause it shows the subtleties of analysis.

Ted Shifrin

Thank you for that edit, @Pedro :D

Mike Miller

@Pedro Well, you're an expert in that.

Pedro Tamaroff

@MikeMiller Expert? Hardly.

Mike Miller

Oh, you edited.

I don't know if you're an expert in the subtleties of analysis.

Ted Shifrin

22:18

grins

We're all going to get banned, @Mike.

skullpatrol

been there done that today

Ted Shifrin

Well, @Pedro, now I no longer know what to believe. I'll ponder more after dinner.

They banned you, @skull?

skullpatrol

@TedShifrin yep

Ted Shifrin

Mazltov!

skullpatrol

Ted Shifrin

22:20

I'll be back later.

skullpatrol

later

Subtle, Subtly and Subtlety

ಠ_ಠ

Is there any theorem/corollary/anything that says if $f$ is differentiable at a point, then all the directional derivatives at that point in any direction exist and are also equal to the same value?

Alec Teal

@skullpatrol get in that room

Daniel Fischer

@ಠ_ಠ If $f$ is differentiable at a point, all directional derivatives exist there. But they are in general not all equal.

Gabriel R.

22:35

@DanielFischer Can you check this (long) proof ? math.stackexchange.com/a/790946/66096

Daniel Fischer

@GabrielR. Too long for today, I'm going to bed in a couple of minutes. I'll look tomorrow.

ಠ_ಠ

Okay, thank you @Dan

Gabriel R.

Alright, thanks in advance @DanielFischer

Pedro Tamaroff

@GabrielR. The roots can be complex.

You're introducing order.

Oh.

It says real.

Gabriel R.

@PedroTamaroff no you misread

Pedro Tamaroff

22:40

The you can be complex, but the OP wants real roots.

Daniel Fischer

@PedroTamaroff Gabriel is the OP.

Pedro Tamaroff

@GabrielR. Unless you made a very stoopid error, it looks like a promising idea.

skullpatrol

@PedroTamaroff are you going to blame me for Mariano not coming to the chatroom too?

Gabriel R.

I got a Wolfram evaluation for $n=4$ running for 2 hours and it just crashed...

ಠ_ಠ

22:59

It says I am disconnected from the chat...ping anyone?

Gabriel R.

@ಠ_ಠ same here, plus the main site lags/cuts down

ಠ_ಠ

23:13

Okay thanks so it's not just me

hichris123

@STajbakhsh It’s not you - an unknown number of users are not getting proper routes to our data center right now.

Tweeted by StackStatus on May 11, 2014 at 11:03 PM in reply to STajbakhsh

We are aware of connectivity issues to our New York data center. Internap is having a device issue upstream they’re working to fix ASAP.

Tweeted by StackStatus on May 11, 2014 at 10:59 PM

^^ @ಠ_ಠ

ಠ_ಠ

Oh, thanks @hic

I live in NYC

hichris123

Yeah, stuff's even been down for me (midwest).

skullpatrol

I'm sure glad they spend their time redesigning the profile page and not the important issues >8(

¯_(⊙︿⊙)_/¯

ಠ_ಠ

23:41

¯\_(⊙︿⊙)_/¯

Gabriel R.

@ಠ_ಠ how is it in NYC ?

ಠ_ಠ

@Gab It's sooooo hot

@Gab I don't even have an air conditioner

Gabriel R.

@ಠ_ಠ how many celsius ?

I thought every American had air conditioning lol. Are you in an apartment ?

ಠ_ಠ

@Gab Yes but some Americans are poor. I live in a housing project provided by the government

@Gab 25C but I am sensitive to heat. I sweat buckets at any temperature above 20C

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