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Jan
5
comment Calculations for grid based games
What is a "move"? Does the grid start empty and you place objects to create matches..? Or does it start filled and you swap pieces? Is it partially filled and you move the pieces around...? Where do the new items appear when the old ones vanish?
Jan
5
comment Calculations for grid based games
It's not at all clear to me what a "grid game to match items in chains" is. Is this a one player game? Two player? Do you place the items wherever you want? What are the "items"?
Jan
5
answered Reflected rays /lines bouncing in a circle?
Jan
4
comment Solving $e^{iz} = 1$
I believe this is only valid for real $z$. Instead the OP should use $e^{x+iy}=e^xe^{iy}$ and then apply Euler's formula.
Jan
4
comment Has this equation appeared before?
Does it arise in any particular context?
Jan
4
revised What are Different Approaches to Introduce the Elementary Functions?
deleted 153 characters in body
Jan
4
answered What are Different Approaches to Introduce the Elementary Functions?
Jan
4
comment Is something wrong with my confidence interval for a Binomial variable?
@AndréNicolas Does my method at least generate a valid confidence interval, or have I misunderstood the definition of a confidence interval? Because usually a confidence interval is defined as a random variable depending on $X$, but mine is constant.
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?