Should I make my quest for an advice a proper Math.SE question ?

Hi @TedShifrin

hi @Karim

Salut @Hippa

@TedShifrin o/

so yeah I made the argument fully rigorous yesterday and translated some of the ideas used there to the question I asked check it out math.stackexchange.com/questions/1357997/… @TedShifrin

proving stuff using open balls you get a feel of the real line

which in turn you get feel of real numbers which is nice

@Karim: I don't like your writing style. You make a claim that $r=$ something. But you've never explained what $r$ should be. Also, ultimately, if $y=1/k$ for some $k$, your $r$ ends up being $0$, which is no good. Someone else pointed that out. Also, you say you're proving this only using point-set topology. There is nothing to do with topology in here. It's just basic inequalities with real numbers.

You need to reread your own arguments several times and ask if they're written concisely and in an organized fashion.

alright

Notice that what you are in fact trying to implement is conceptually what I said: You're taking $r$ to be the distance from $y$ to the set in question (and if $y$ is in the set, you're removing it first before you do that distance). Then there can be no point within the ball of radius $r$ centered at $y$ by the definition of distance.

yeah

You should not need to do all these separate cases once you understand this.

I understand your explanation is according to how strants did it that is easy to generalize too but problem with this is that that way I feel is not really deep enough rather than directly working with the set itself, however I do agree it is more elegant and easy to generalize to problems similar to this one.

"not really deep enough"?

As you mature as a mathematician, you want to try to avoid case-by-case checking whenever there's a better argument. Sometimes you have no choice. But usually you do.

I see

I thought if I deal directly with the set case by case I would increase my geometrical understanding of the real number line

but yeah I agree with you

There's not much going on other than what I've been saying. But ... as you young'uns say, whatever ...

oh oh, mr legos is back already?

Some of us have no idea what you're talking about, @iluso, sorry.

Bed is done. We struggled with one corner for a long time. There's these fancy screw-like objects, and for three of the corners, you tighten by turning CCW. Asymmetrically the last side you turn CW. We never even thought to try this until we made a mistake.

That seems nutso, @MikeM.

Are there destructions that come with it, or a diagram showing the screw thread?

I remember enjoying these projects somewhat when I was your age, but now I have neither the patience nor the body strength to deal with it.

There's schematics but not detailed ones. It's a big puzzle! We think it was a manufacturing error.

LOL

Well, you gets what you pays for :D

I remember all those Sears schematics when we would have to assemble lawn fertilizer spreaders and other such things ...

@MikeM: I guess the saying "You made your bed; now you can lie in it." really is applicable.

@TedShifrin Well I have this $H_d$ expression and I am searching a way to simplify $H_d(n,k) / k!$. I though it was possible to reduce it since $H_d$ contains $k!$ too. Sorry if I'm not clear

@iluso: There are a few people here from time to time who may know what you're talking about. But you're going to do better posting questions on main.

@TedShifrin Ok, thanks !

@PaulPlummer That's another thing I don't understand: how can there be a countable model of ZFC? Does ZFC not imply uncountable sets, e.g. the set of all real numbers? Or can uncountable sets somehow exist in countable models?

The model of ZFC thinks that the set of reals would be uncountable (all models of ZFC do), but looking in from the outside that set of reals is countable @Kyth'Py1k

hm

what do you mean

@PaulPlummer

looking from the outside ?

that is crazy if we consider reals as countable how can we list them

Well that set of reals would not be a set of reals in a different model that could tell it was countable

@KarimMansour

oh

oh I see

Ugh, 5 week class final graded. The results: An emphatic not good!

yeah intuitively speaking we in another model if somehow can exhaust or represent real by counting it

that means we would have enough numbers in our system to represent PI and other numbers like it such that we create one to one correspodence

that would be very weird set

@PaulPlummer

Given the definition of the Walsh transform shown here: en.wikipedia.org/wiki/Bent_function, how can I compute the inverse transform?

@Ted: I bought a mattress second-hand. Guy said it was a queen. It's a twin. Completely worthless.

Ok, full, not twin.

Oh, full is what I have for my second bedframe which isn't moving, @MikeM. Yeah, worthless if you have a queen-size frame. It behooves one to measure :(

@pjs36: I've been there, I'm afraid.

I just hadn't expected that someone would just be wrong about the size of their bed...

there's not a huge difference between full and queen ... and it turns out there are two kings — I had never heard of California king before I started condo-hunting a few months ago

@TedShifrin

Hello.

mr @Pedro :) belated happy birthday, sans jinx :P

Hehe. Thanks.

Any thoughts about my question on Bartlett's paradox? math.stackexchange.com/questions/1356796/…

Happy Birthday @PedroTamaroff :)

Even any good refs would be helpful

So, @Pedro, have you figured out new ways to do that "expected number of cards before first ace" question you helped me with?

@TedShifrin I confess I never thought about it again. =)

Now that I know some probability I could try.

Yeah, but now you're taking probability :P

There are some good ways using indicator functions, I think.

So, mr @Pedro, how does it feel to be old and over the hill now? :P

@TedShifrin Ah, I think I should just dig a hole in the earth.

Inside ZFC the reals are always uncountable because of Cantor's theorem. But uncountable just means there is no injection into the naturals, so all that is saying is that some function does not exist in ZFC. A ZFC model can be countable, but inside that model there is still no injection from the reals to the naturals. @KarimMansour

Well, that'll give you more exercise than tennis :P

@PaulPlummer "A ZFC model can be countable"?

yeah but there would injection into other thing right ?

@PaulPlummer

A model of ZFC (if such a thing existed) @PedroTamaroff

is there such a thing ?

or is it just hypothetical

any reference?

well, @Pedro, I have just 10 days or so left as a Georgia resident ... :P

Are you taking a big crate of peaches with you as a souvenir, @Ted?

nope ... my local peach farm got frozen out this winter and has no crop :(

No wonder you're leaving then!

Well, I shall miss the peaches ...

It is a hypothesis. @KarimMansour

I see

@TedShifrin Oh. Well, start packing some sunscreen and water. =)

Yeah, the water is the issue ... If you visit, bring your own :P

Why is the water an issue Professor?

@Ted: It makes sense. California is famous for its queens - why not kings, too?

Précisément, @Mike :)

Droughts of epic proportion, @skull.

@Pedro: Hope we get to revisit multivariable analysis some day, when you tire of all this functorial algebra :P

Speaking of, @Ted, I ordered your Multivariable book from the library, one of those inter-library loan deals. I'm looking forward to it - much to learn!

well, @pjs36, I hope you're not too disappointed.

Probably only when they take it away from me!

Ha ha ... For your slight amusement, there are also the YouTube lectures.

So maybe in a few days I'll be done moving in (and getting the right sized mattress... grr) and can actually get back to work.

It'll be over in finite time, @MikeM. I am looking forward to 4-6 weeks from now.

My roommate has a copy of your algebra book on his bookshelf, I saw.

Well, that's not so surprising.

He presumably has a copy of the Multivariable, too.

I will get a copy of your book @TedShifrin too

the multi variable one

I don't want to feel like an advertising billboard in here.

also, finite can be a very long time... I don't want to be unpacking up Til my funding runs out.

I suspected you'd take issue with that.

By implication, I expected your finite time to be less than my 4-6 week timeline.

I don't see your multi variable on his shelf, but I probably didn't look hard enough. He has Palais's book on Atiyah-Singer I should probably steal...

...friends don't steal from friends :)

pal

So I was talking to my academic advisor about applying for the Budapest Semesters in Mathematics program, has anyone in here done this program? If so what should expect from it?

@TedShifrin When I get to diff. geo, I will.

@MikeM: I think intraapartment borrowing doesn't count as stealing.

Just so long as you don't forget me completely, @Pedro :D

@ixsetf I've heard nothing but good from the folks who have done it

If you're primarily interested in discrete mathematics, @ixsetf, it should be well worthwhile if you get admitted :)

@Ted: Well, I probably have enough to do this week anyway... and the next...

I'm betting the other book is at school, @MikeM, 'cuz he's teaching multivariable this fall. I've forgotten what text he finally decided on, but I assured him it shouldn't be mine.

Simply for the price alone, or for other reasons, @Ted?

@pjs36: For a year-long course, the price isn't that horrible, given how much stuff is in there, but I am not proud of book prices. No, just not appropriate for the standard "honors multivariable" for freshmen.

@TedShifrin That is good to hear, assuming I get in. Is the program particularly competitive?

I am not that knowledgeable, @ixsetf, but my impression is that it is.

Ah, I see. I was just curious, I hope you didn't mind my asking @Ted.

Of course not :)

I don't remember what he's using.

Mostly I'm just putting off actually entering grades and seeing how the whole course shook out. Maybe things will go better for the 8 week class!

In general, math courses that meet 2 hrs/day 5 days/wk are a disaster, @pjs36. Students just can't absorb/process at that pace, let alone spend 4 hours a day on homework on top of it.

Yeah, I strongly suspected that was going to be the case. But test 1 was promising, and I thought "Well, maybe not this time..."

We shouldn't even think of offering these super-fast-paced classes. Sigh. Administrations wanna make money.

I just can't help but feel that somehow I should have motivated everyone to try harder and stay on top of things. But I guess that's what beer's for :)

@pjs36: Most of my career I've motivated students to work unbelievably hard, but the last few years I've been unable to do so with many of the students. I don't know what to do any more.

(I suspect this is why everyone wants your books, @Ted, no billboard effect, by the way). Yeah, teaching lower level classes has been rough, there's definitely an art to it that I haven't figured out

I know you've had your share of higher-level stuff, of course

Yes, @pjs36. The lowest courses I've taught were freshman precalculus. I did it a few times (voluntarily) and actually enjoyed it. But I was pretty spoiled. Although I taught courses where I scheduled something like 8-10 office hours/wk, which no one else ever would do.

@TedShifrin Hey I wanted to ask if you would consider zero as a positive number.

NO.

If it were, it would also have to be negative (by definition, negative numbers are the additive inverse of positive).

@TedShifrin ok then let me ask you this question.

I bet the answer is "trichotomy"

LOL, @pjs36

I don't need any encouragement, y'know :P

well, just don't start an episode of horrid puns

@TedShifrin actually never mind, you answer helped me answered a certain question.

This desk is the most mysterious thing I've ever built. I swear these are actually instructions for constructing an Escher sculpture.

pjs36 wanted your question, @Deathslice.

oh, so if you go up along the desk, you end up underneath? @MikeM

OK, I'm outta here. Good luck @MikeM

Later

See you next time, @Ted

You probably do all your work inside the drawer, @Ted.

Wb @robjohn

Hello!! Is someone of you familiar with the undecidability of existential theories of rings and fields?

Existentialism is down the hall, first door on your right :P

Hi @robjohn Remember this limit? $\displaystyle\lim_{(x,y)\to(-1,0)}\frac{y^4(x+1)}{|x+1|^3+2|y|^3}$. Well someone evaluated it like this: 'If $y\neq0$ then $$|f(x,y)|\leq|x+1|\dfrac{y^4}{2|y|^3}=|x+1||y|/2$$ What do you think?

@Cristopher what do you think? Do you see anything wrong with it?

@robjohn Well, I don't... but it surprised me because it's a much simpler way to evaluate it

@Cristopher I was just gave the minimum... There are other bounds.

I used the AM-GM which is quite useful

@robjohn Oh, so you were aware of that solution too. I see. No doubt the AM-GM is useful.

@robjohn Epsilon delta proof of $\displaystyle\lim_{x\to1}\ln(x)=0$. We have $|x-1|<\delta$ whenever $|\ln(x)|<\varepsilon$. Then $e^{-\varepsilon}-1<x-1<e^{\varepsilon}-1$. Would $\delta$ be equal to $e^{\varepsilon}-1$ in this case?