Jack M
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 Apr 12 comment Finding a Mathematical definition of a Discrete Time Game @MathNerd So if it's in discrete steps, why are you modelling time by a real number? Just use an integer. Apr 12 comment Finding a Mathematical definition of a Discrete Time Game I feel you've left out some details as to how the game works. Do the players move in discrete steps? If not, do they move at constant speed, or can they accelerate and decelerate? If motion is continuous, then when is a tank considered to leave one square and enter the next? If a square is shot at and a tank is partially on that square, is that a hit? Apr 9 accepted Why does the Elo rating system work? Apr 9 awarded Nice Question Apr 8 comment Why does the Elo rating system work? Great, thanks. So we basically model chess players with a weighted directed graph (the weight on the edge A -> B being the odds that A beats B), with the transitivity assumption you described. That seems like quite a non trivial assumption. Do you know a reference with more discussion on the details and the validity of the model? Apr 7 comment Why does the Elo rating system work? I haven't read the papers in full yet, but the one which gets closest to answering the question still seems to miss the mark. It helpfully describes a model in which we think of chess players as generating normally distributed random numbers, and the winner of a game as being the one that generates the larger number, but then when it gets to the formula for the probability of one player winning the game (page 10) it just calls it an assumption of the model. I find it hard to swallow that such an arbitrary formula is literally just assumed with no justification. Apr 7 asked Why does the Elo rating system work? Apr 6 comment Area of a circle $\pi r^2$ The point is, you are the one imposing the interpretation on $r^2$ as being the area of a square. Really, $r$ is just a number. And $r^2$ is another number. And if you multiply that by $\pi$, you get yet another number, which happens to equal the area of the circle (which is also just a number). Apr 6 comment Area of a circle $\pi r^2$ I have nine pens on my desk. Nine is $3^2$. This is the area of a square with side length $3$. How can a square become pens?? Mar 24 revised What is the difference between numerical integration and Riemann integration? added 569 characters in body Mar 24 answered What is the difference between numerical integration and Riemann integration? Mar 23 awarded Popular Question Feb 25 awarded Revival Feb 20 revised Multiplication without figures edited tags Feb 11 comment Comma placement inline math @BrianO The first fragment can be read that way as well, imagine there's an implicit "where" or "with" after $f(x_j)$. Feb 11 comment Comma placement inline math @BrianO I believe the OP is saying that you can read the sentence as "Given $f(x_j)$, where $j=1, ... N$, - our goal is to...". In this case the comma is clearly recommended. Feb 10 answered Alternative Proof that $\sqrt{p}$ is Irrational when $p$ is Prime Feb 10 answered Can sum of rationals be irrational? Feb 10 comment Can an infinite sum of irrational numbers be rational? And the linear independence of the terms follows from the transcendence of $\pi$, which is the cleverest part of the answer. In fact any power series with rational coefficients, evaluated at a transcendental value but having a rational sum, would have done. It makes me wonder if there are "super-transcendental" numbers, which are not roots of any power series with rational coefficients. Feb 9 comment How limiting/ heavy is the “triangle inequality” assumption? If you drop the triangle inequality, basically all you have left is a symmetric function from $X^2$ into the positive reals. The triangle inequality is responsible for every important property of a metric.