Mark S.
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 Apr 16 answered What's the intuition behind the identities $\cos(z)= \cosh(iz)$ and $\sin(z)=-i\sinh(iz)$? Apr 14 comment Is this translation into symbols correct? What you wrote seems to be saying that F doesn't prove $\varphi$ nor does it prove the number corresponding to $\neg\varphi$ under some encoding. It doesn't really make sense to talk about proving a number. Also, I doubt your use of $\top$ commonly means whatever you're trying to represent with it. Finally, you may want to encode the "any" in "any foundation" somehow. If you want to cheat and see how logicians actually write the first part of the statement formally (though the meaning of "true" is slightly warped), you can see math.stackexchange.com/a/980983/26369 . Apr 13 comment What's the intuition behind the identities $\cos(z)= \cosh(iz)$ and $\sin(z)=-i\sinh(iz)$? What definition of cosh and sinh are you using? Everything sort of falls out from the exponential function being it's own derivative, but if you want a different explanation you'll need a definition (if intuitive) for cosh and sinh to start from. Apr 13 comment Why polynomial functions f(x)+g(x) = (f+g)(x)? As a side note, if this is a first linear algebra text it probably doesn't get into algebras. $f\cdot g$ is unlikely to be defined and if it is defined, it might mean an inner product via an integral or something. In any other intro to rigor text I would agree with you. Apr 10 revised Function that maps the “pureness” of a rational number? edited tags Apr 9 reviewed Approve Functions can be represented by several formats or they are immutable? Apr 9 comment How do you call a 3d convex shape made of 8 arbitrary points? It sounds like you may also be interested in the "convex hull" of 8 points. Apr 9 comment “Binary-Like” Function?; In Consecutive Products as Multi-Factorials… Eric probably knows this, but for anyone new to the complex number solution, every periodic sequence can be written using those same exponentials (the roots of unity) but with different coefficients. The technical reason is the linear independence of the sequences of the first n powers of the n nth roots of unity. Apr 9 comment Visually stunning math concepts which are easy to explain @PyRulez Using your hue idea I made this in Mathematica: i.imgur.com/xdaCEfD.png Code was: ArrayPlot[Table[Table[Mod[m*n, 512], {m, 0, 511}], {n, 0, 511}], ColorFunction -> Hue, ColorFunctionScaling -> True, AspectRatio -> Automatic, Frame -> False, PixelConstrained -> True, ImageSize -> 512] Apr 7 comment Number of functions from n-element set to {1, 2, …, m} Write down the functions from a 2 element set to an m element set to answer the first question. If that's too abstract, set m equal to a small number first. Apr 6 awarded Fanatic Apr 4 revised show that ∀ x P ( x ) ∨ ∀ x Q ( x ) is logically equivalent to ∀ x ∀ y ( P ( x ) ∨ Q ( y )) . (Domains for x and y are the same). edited tags Apr 3 answered Dichotomy in the number of regions on a plane formed by an infinite number of lines Mar 29 comment Topological space $\{a,b\}$ with topology $T=\mathcal{P}\backslash\{b\}$ path connected Since not every element of $[0,1]$ is in $\{a,b\}$, $\gamma (x)=x$ does not define a path in $A$. Mar 29 comment Topological space $\{a,b\}$ with topology $T=\mathcal{P}\backslash\{b\}$ path connected name any function between a pair of endpoints and see if it does what you want. Mar 29 comment Topological space $\{a,b\}$ with topology $T=\mathcal{P}\backslash\{b\}$ path connected Have you tried any such functions and the definition of continuous? Mar 27 comment Need help to visualise Topological Puzzle For a reference, it's video #10 from page.mi.fu-berlin.de/polthier/video/VideoMath98/index.html Mar 27 comment balancing stats for equality Could you describe in more detail how the game works? Is using the shield a move? And you have to be clear about what you mean by equal foe. Do they play randomly? Do they play well as if the know their opponent's moves from the start? Do they play well but have to observe the opponent's moves? Do you have a metric in mind for "playing well"? Etc. Mar 26 comment Existence of spatial equilibrium I admit I don't know the definition of a "spatial game", but a Google search pulled up "Finding a Nash Equilibrium in Spatial Games is an NP-Complete Problem" at ideas.repec.org/p/kud/kuiedp/0219.html , which may or may not be helpful to you. Mar 26 revised Misere nim, 2nd player winning strategy proof by induction edited tags