2,583 reputation
1725
bio website noldorin.com
location London, United Kingdom
age 23
visits member for 3 years, 9 months
seen Apr 13 at 17:30

entrepreneur; graduate in mathematics / theoretical computer science / theoretical physics; polymath-in-training

based in London, United Kingdom


Apr
13
comment Does factor-wise continuity imply continuity?
Interesting question. Does the converse hold by chance? (I'm guessing not.)
Apr
7
comment Rudin against Pugh for Textbook for First Course in Real Analysis
That's great, thank you. I'm not sure d'Alembert meant precisely the same thing you did in your above answer, but I do think both are very worthwhile pieces of advice!
Apr
7
comment Rudin against Pugh for Textbook for First Course in Real Analysis
Ah right, interesting. Well, please do check if you wouldn't mind; I'd appreciate it.
Apr
6
comment Rudin against Pugh for Textbook for First Course in Real Analysis
Interesting quote. I like it, and also happen to agree. Have any source on it? A quick Google turns up zilch.
Mar
29
comment Proving $\big(n!^{\frac1n}\big)_{n\in\mathbb N^*} \to \infty$
What's $\mathbb{N}^*$? Never seen this odd notation before.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: Many thanks!
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: Are there any other insights now, or is all that remains filling in the details of the proof?
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Yeah. And this is indeed the case, because of the positivity law of the inner product, as you hinted at earlier...
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Ah yes, very good. Been a while since I did all the conics stuff, but that strongly rings a bell for me.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Looking at the implicit Cartesian equation for an ellipse, it would now seem I need the condition $b^2 < ac$. Tell me if I'm jumping the gun though.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Okay fair enough. I guess that's just how I expected it, but indeed, that convention sounds right.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
I suppose this should remind me of the equation of an ellipse now?
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Hah okay, you're a stickler, but I'm happy to oblige if it progresses us... Is $||(x, y)||^2 = \langle (x, y), (x, y) \rangle = x^2 a + 2xyb + y^2 c$ any better? :)
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: Okay, I see the problem. I made a bit of a muddled analogy with the expansion of the square of a binomial... (never had the patience for rote calculation, even when not doing it leads me astray). So I believe it's correct if you replace $a^2$ with $a$ and $c^2$ with $c$ above?
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
Yeah that's precisely what I did, hmm... let me double check.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
It's just expanding the inner product using its laws...
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
I've done a good deal of linear algebra. Is that not even close?
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: Typo.
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: Ah okay. Well in that case, $||(x, y)||^2 = \langle (x, y), (x, y) \rangle = x^2 a^2 + 2xyb + y^2 c^2$, no?
Mar
28
comment Geometric conditions equivalent to a set being the unit circle for some norm
@WillJagy: I don't quite get your suggestion I'm afraid. What are a, b, and c except arbitrary assignments to variables?