Reputation
12,122
Next privilege 15,000 Rep.
Protect questions
Badges
1 23 58
Newest
 Yearling
Impact
~212k people reached

Jan
4
asked Is something wrong with my confidence interval for a Binomial variable?
Jan
4
comment Is there a meaningful distinction between “direct” and “iterative” methods for solving equations?
The distinction is exactly what you say in your question: an iterative method is not a formula expressed in radicals. If I say $x=1+\sqrt 2$ I have expressed $x$ using a formula expressed in radicals. If I say "$x$ is the limit of $x_{n+1}=f(x_n)$ when $x_0\in[-1, 2]$, I haven't.
Jan
4
comment Does a game need below-average players
@FlorianPeschka If we have $n$ players, and they all have greater than $0.5$ win rate, then the sum of their win rates (which must still be equal to $1$) is at least $n0.5$, which is even worse than what we get with $2$ players!
Jan
4
comment Is collapsing considered a legitimate proof?
@DanielR.Collins The $S$ in this answer has nothing to do with the $S$ in the question.
Jan
3
awarded  Nice Answer
Jan
3
comment Is collapsing considered a legitimate proof?
@S.Mo I rewrote the proof to use a structure closer to what you're used to.
Jan
3
revised Is collapsing considered a legitimate proof?
added 191 characters in body
Jan
3
comment Is collapsing considered a legitimate proof?
@S.Mo That is a correct proof by induction, but different from the one I gave. The proof by induction I give in my answer is directly modeled on the "collapsing" method you used in your question.
Jan
3
comment Is collapsing considered a legitimate proof?
@S.Mo In induction we have a predicate $P(n)$, that is, a true-false statement into which we can plug $n$ like a variable, for example, an equation involving $n$. We then show that if $P(n)$ is true for any $n$, then $P(n+1)$ is true. Using phrasing like "show that it resembles" makes it seem like induction is just a method of shuffling symbols around.
Jan
3
answered Is collapsing considered a legitimate proof?
Jan
3
comment Prove the roots of a complex polynomial are imaginary
@inya Do you understand basic polynomial algebra concepts like polynomial long division, the remainder theorem, etc? Khan Academy's "Polynomial Arithmetic" course covers it, or you could look for a textbook on (modern) algebra and skip to the chapter on polynomials. If you understand all these concepts then I think the Wiki article on the Polynomial GCD should be sufficient if you soldier through it.
Jan
3
comment My proof that $S_n/\sqrt n$ does not converge in probability
I don't understand your construction though. To what are you claiming your $S_n/\sqrt n$ converges in probability?
Jan
3
comment My proof that $S_n/\sqrt n$ does not converge in probability
In response to your last paragraph: Yes, I think for this reason this proof (were it valid) would necessarily have to be posed as a proof by contradiction (unlike many proofs by contradiction which can be rephrased as direct proofs of contrapositives). You have to assume the sequence converges in probability to $Z$ in order to even be able to say what $Z$ is.
Jan
2
accepted An algorithmic approach to constructing the real numbers
Jan
2
comment My proof that $S_n/\sqrt n$ does not converge in probability
@Winther I don't think that really answers the question - my question is specifically about whether the approach I used is valid or can be modified to be valid.
Jan
2
comment Does a connected countable metric space exist?
Very intuitive proof. You're using a result that says the only connected subsets of $\mathbb R$ are the intervals, I guess?
Jan
2
comment An algorithmic approach to constructing the real numbers
So you're saying there's no way to patch up the hole in the algorithm I proposed in my answer?
Jan
2
asked My proof that $S_n/\sqrt n$ does not converge in probability
Jan
2
comment What is the fundamental matrix solution?
Do you know about matrix exponentials?
Jan
1
awarded  Nice Answer