Mathematics - 2021-04-13 (page 3 of 3)

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dc3rd

23:02

So I'm trying 13* from sec 2.2 @TedShifrin It is the one that asks to prove that if my sequence is Cauchy, then all points lie in some ball centered at the origin. .......

I don't know if I'm trying to find something that isn't there, but given that my sequence is Cauchy, that would mean the distance between the points is going to $0$.

On the other hand claiming that all the points lie in some ball around zero means the cauchy sequence is converging to $0$......

Ted Shifrin

Nonsense.

dc3rd

After I wrote that. realized it wasn't even stated that the sequence converges

Ted Shifrin

The ball could have radius 1,000,000.

You're eventually going to prove that it converges.

dc3rd

yea that's 14c)

I had written something else, but I don't think it can be the case. So by definition I'm given $x_{k}$ is Cauchy, as such there exists $k,l > K$ such that $||x_{k} - x_{l}|| < \frac{\epsilon}{2}$. If I'm trying to show that all points line in some ball at the origin then given that $x_{k}$ is cauchy:

$||x_{k} - 0|| \leq ||x_{k} - x_{l}|| + ||x_{l} - 0|| < \frac{\epsilon}{2} + \frac{\epsilon}{2}$

Ted Shifrin

23:33

Huh?

dc3rd

I didn't think so either.

Ted Shifrin

Be more self-critical when I've already said Nonsense. I will get more blunt.

leslie townes

\| is preferable to ||

dc3rd

$\|$ .....ah

leslie townes

that's my valuable contribution here. also no need for the {} if it's just around one thing in those subscripts. i will submit an invoice for half of the time that i have saved you with that.

i mean \| and || look exactly the same unless you've done latex too long and then the spacing on the || begins to look funny to you. particularly if you have a scalar right in front of the first | and the spacing of the line is just so.

it's not as bad as < versus langle. that should look like a disaster to anybody.

Ted Shifrin

23:38

Q for you, leslie. Do attorneys have something analogous to residency after they pass the bar? How do you find out how to actually argue a case in a courtroom?

leslie townes

the short answer is no. at a large law firm there's a somewhat ritualized practice where you spend a couple of years maybe going to court at all, or just watching, and then slowly they get you doing other stuff that's like going to court (deposing witnesses or examining witnesses). at a small law firm they might just throw you into the deep end. or you might never argue a case in court.

some firms can go a year without going to trial, and not just bad ones either

hearings in front of a judge, particularly over minor issues, are a good start. i don't think you have anyone arguing in front of a jury straight out, but there's no rule against it.

there's no rule against me representing someone in a murder case tomorrow. that's kind of weird to me.

there are a lot of bad ones, sadly. and the rules of discipline are pretty attorney-favorable.

for some reason. also the statute of limitations on malpractice claims is really short. i wonder why that is.

Ted Shifrin

Just like all the incompetent teachers on university faculties.

Sigh.

leslie townes

it's very similar. also in the law there is an enormous amount of substance abuse so people are dealing with that.

i didn't see as much of that in universities. just people abusing notation

Ted Shifrin

Thanks for restoring levity!

dc3rd

Hint?.....Working backwards I know that for all the points to lie in ball centered at the origin it means $\|x_{k} - 0\| < \epsilon$. From the front I have the Cauchy condition.