Jack M
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 Jan 6 comment Proving set property in real analysis There's almost an algorithm for proving that sets are equal to one another, in basic set theory. If you need to prove that $X=Y$, first prove that $X\subseteq Y$, then prove that $Y\subseteq X$. If you need to prove that $X\subseteq Y$, then write "Let $x\in X$" and try to prove $x$ is in $Y$. Jan 5 comment Can we assign a number to each theorem stating its complexity? @PaoloFranchi The notion necessarily has to be relative to a given theory. In a theory in which Fermat's last theorem is an axiom, FLT has a very different complexity than in Peano Arithmetic. Jan 5 answered Calculations for grid based games Jan 5 comment Calculations for grid based games Okay, I see now. So what is it exactly that you want? You want a way of assigning a "difficulty score" to any given initial state of the board? Or a way of fixing a reasonable "target score" for a given board? 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.