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Dec
27
asked How can I prove $x_{n+1} = e^{-x_n}$ is convergent?
Dec
26
answered Let $n ∈ N, n ≥ 1$. Prove that $4^n + 6n - 1$ is divisible by $9$.
Dec
25
answered Why do we do mathematical induction only for positive whole numbers?
Dec
23
revised Describe the rational points on $3x^2 + y^2 = 4$
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Dec
22
comment How to generate random points on a sphere
@BrianM.Scott Do you have a reference for the geometrical theorem you mentioned?
Dec
19
comment what does it mean for a function to be riemann integrable
To be clear, saying "the sums converge to $I$ as the mesh gets finer and finer" means "for any $\epsilon > 0$, there is a $\delta$ such that as long as the mesh is less than $\delta$, the sum is within $\epsilon$ of $I$".
Dec
19
asked Is convergence in law compatible with arithmetic?
Dec
15
comment Simulating Bernoulli processes using several random binary strings
It's not entirely clear what the question is (it's not clear what phrases like "the resulting strings" refer to, for example) and it contains some irrelevant details - for instance, we don't really need to hear about the "square site percolation coefficient" if that's not part of the problem. Ideally you would have begun with something like "Let $B_n$ be independant bernouilli random variables whose probabilities are expressible as integer percentages..." and asked a specific mathematical question about them. As you noted under my answer, I wasn't quite able to understand what you were asking.
Dec
14
answered Simulating Bernoulli processes using several random binary strings
Dec
12
answered What is an intuitive definition for “conjugate” in Group Theory?
Dec
8
comment The “pepperoni pizza problem”
I would recommend trying to solve this problem for a one-dimensional pizza first.
Nov
30
comment Is this alternative notion of continuity in metric spaces weaker than, or equivalent to the usual one?
Not only is your definition equivalent, this kind of thing is used implicitly fairly often, particularly in measure theory and probability theory, where for technical reasons you may need to replace a "for all $\epsilon$" with a "for countably many $\epsilon$".
Nov
29
comment Determine if a 4-tuple exists
@Analysis15 Let $A$ be the operation by which we go from one tuple to the next, e.g. $A(4, 0, 7, 1) = (2, 0, 0, 3)$. We know $A$ is invertible, call its inverse $A^{-1}$, that is, $A^{-1}(2, 0, 0, 3) = (4, 0, 7, 1)$. Let $x_0=(2, 0, 0, 3)$, then we're looking at the sequence $A^nx_0$. Since there are only finitely many possible tuples, we must have $A^nx_0=A^mx_0$ for $m$ and some $n>m$. But then $A^{n-m}x_0=x_0$.
Nov
27
comment Prerequisites for proving basic arithmetic algorithms
Would you mind sharing the title of the book you're working from?
Nov
24
revised Two formulae for $\pi$, probably known?
added 2 characters in body
Nov
20
awarded  Nice Question
Nov
17
comment Puzzle with twins
I would simply say that the husband's will doesn't cover this situation, so there's no "correct" solution.
Nov
14
comment Can this argument in the calculation of $P(X+Y<a)$ be made rigorous?
Could you provide some more details? I think step two is just a standard change of variables, but what exactly are you doing in steps 1 and 3? What definitions/results are you using to expand the probability as a double integral, and to collapse the double integral back into a single integral?
Nov
14
asked Can this argument in the calculation of $P(X+Y<a)$ be made rigorous?
Nov
11
comment Why this doesn't contradict Monotone and Dominated Convergence Theorem?
Well, I suppose the $f_n$ are neither monotone nor dominated.