Well, it's not easy to establish a direction relationship. What I'm describing are more correlations that you see when trying to minimize particular quantities. It's entirely possible to have excessively high values in all three quantities.
There are also situations where the correlations break, I should mention.
For more context, the tournament is for this game: https://store.steampowered.com/app/558990/Opus_Magnum/ The three quantities are "how fast the solution to a puzzle is, the total cost of parts used in a solution, and the area that the solution occupies on the board"
Obviously, using fewer parts results in a smaller board area used, and should also result in cheaper solutions.
I am probably lacking the right terminology to convey my point (order preserving bijection is perhaps what i am getting at?)
but basically $z\mapsto 1/z$ doesn't preserve order. I.e. I probably made the mental error to think that $0$ should map to $0$ (since the line itself remains invariant)
it's sorta like: I was just telling my calculus kidlets today that $f'=g'$ only implies $f=g+c$ when the domain is connected ... if you have different components, the $c$ can change from component to component.
I offered to "teach" my best student this year my multivariable math class as an independent study course next year. We'll see if he's good enough to do that.
Well, interestingly, my ex-colleague at UGA who was unquestionably a star researcher (Russian) was too easy on kids, because he didn't want to be bothered.
@Dair: This depends on country, of course. But, generally, yes, econs need some computational multivariable, but only serious math if they're going on to graduate work.
Graduate econ really does use some serious math analysis.
@TedShifrin Btw, I started messing around with some math stuff recently today. Probably wasting my time, but it was fun lol. Been doing too much CS started missing the math. :(
@TedShifrin Basically anything. I was looking at some stuff by Euler, in particular the Euler Prime Product theorem and was just wondering if there was a way to generalize it to Gaussian Primes. I basically came up with nothing after a couple hours of working, but found out there was one after extensive google.
Basically I've been a bit tired this past few days. Haven't really been doing a problem solving grind, but just looked at some results and thought: "Is there a way to generalize this?" That's why it's probably a waste of time. Still kind of fun.
It's pretty similar to mine but slightly worse (e.g. i5 instead of i7), and also he has a really wide screen since he usually has two windows open at once
It does seem to start from scratch, though I'll have to look up what those diagrams etc mean. The first few chapters couldn't possibly use a lot of category theory, could they?
I am not interested in the philosophical part of this question :-)
When I look at mathematics, I see that lots of different logics are used : classical, intuitionistic, linear, modal ones and weirder ones ...
For someone new to the field, it is not easy to really see what they have in common fo...
hey, if I have a function f(x) cont on [a,b] and diff on (a,b) and know that f''(x)>0 (so f'(x) is increasing, i.e. f'(b)>f'(a)) and a define a new function piecewise g(x)=f(x)-f(a)/x-a if a<x=<b and g(x)=f'(a) if x=a, then is it true that g'(x)>0 on (a,b) as well?
doing it by cases it doesn't seem like this is necessarily always the case
The cayley graph of Zp X Zp has a square mesh structure. Cayley graph of Zp X Zp X Zp has a cubic structure. How can we call the structure of Zp X Zp X ...X Zp , n times?
The correct meaning is that, when they say (for instance) $\lim_{|\mu|\to\infty}f(\mu,s)=F(\mu,s)$ they mean $\lim_{|\mu|\to 1} \frac{f(\mu,s)}{F(\mu,s)}=1$
That's a perfectly legitimate statement, but the two are very much not synonymous
(You can say that $F(\mu,s)$ represents the 'limiting behavior' of $f(\mu,s)$ but that's not what $\lim$ is supposed to denote)
@astyx going to post this on the talk page:
"The section on "Limiting behavior" states several limits, which are (modulo possible typos) found in Wood 1992. While the title (correctly!) frames these as the limiting behavior of the polylogarithm, the text (following Wood) misleadingly presents them as limits of the polylogarithm. But the polylogarithm either vanishes or diverges in each of these instances. More formally: The text indicates that f(mu,s)->F(mu,s) as mu or s is varied appropriately, when in fact it means that f(mu,s) ~ F(mu,s) i.e. f(mu,s)/F(mu,s)->1 in the appropriate limit. (The only exception is the fifth statement, w…
For a semidirect product between Z3 and Z5 X Z5, where Z5 X Z5 is the normal subgroup, if we consider a cayley graph with respect to a generator set with two elements say s,t, if order of both elements is 3, Why does st^(-1) always belong to Z5 X Z5?
Thanks @LeakyNun and @TobiasKildetoft. I found it in the proof in page numbered 43, in this articlehttps://amc-journal.eu/index.php/amc/article/view/177
