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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