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5h
asked Does the PNT establish a connection between primes and the logarithm?
18h
comment Number of points of accumulation of a sequence
There's a classic theorem that if you walk around a circle in discrete steps of $a$ radians, where $a/\pi$ is irrational, then the set of points that you visit is dense in the circle. This implies that $(\sin(an))_{n\in\mathbb N}$ is dense in $[-1, 1]$, and you can take $a=1$ for a cute example of a sequence with infinitely many accumulation points.
18h
answered Prove that the Gaussian Integer's ring is a Euclidean domain
20h
comment Irrational numbers generated by a deterministic cellular automaton?
I'm not sure why you're so pessimistic about proving that a cellular automata-generated number is transcendental, when you then immediately cite a very similar (and marvelous) result about how finite automata-generated numbers are transcendental.
Apr
27
awarded  Nice Answer
Apr
24
comment Is there a way to write an infinite set that contains only irrational numbers without integer multiples?
More generally, you're relying on the lemma that for any finite set of irrationals, the set of the their integer multiples does not cover the set of irrationals. But this is obvious: the set of integer multiples of any finite set is discrete, but the irrationals are dense.
Apr
21
comment Injective: In what circumstances would there be less than one pre-image of an image?
No, no - of course an "image with less than one (ie, zero) pre-image" is a contradiction, that can never happen. An injective function has no more than one pre-image for each image, but the opposite of "no more than one" isn't "less than one", it's "only one".
Apr
20
answered why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$
Apr
17
comment Is PA the first axiomatization of arithmetic to be discovered?
Euclid sort of axiomatized arithmetic, or tried to.
Apr
14
comment Does this equation my professor wrote actually work?
@hexomino No no, that's not the problem - $(\frac 1 e)^0$ is well-defined. The problem is that for some reason the OP thinks $(\frac 1 e)^0$ should give $0.5$, which it shouldn't - $0.9$ (ish) is correct. How do you figure that's 0.5, OP?
Apr
13
awarded  elementary-number-theory
Apr
12
comment How Are The Graphs Related?
@JebusCrust Then it moves to the left by $c$ units.
Apr
12
answered Concise proof that every common divisor divides GCD without Bezout's identity?
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?