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Apr
4
comment Fastest way to meet, without communication, on a sphere?
Thanks, @Ilmari, I realize now that indeed we can assign "North" and "South" based on the direction of rotation. As for the rest, for me there is in fact a natural (Eurocentric) precedence of North over South, but there's no need to rely on that: As I also say in my answer, limiting the search to a finite number of points is far better than scanning the entire surface.
Apr
3
comment Diagonalizing a power set
Should that be "... where for each $x \in S, f(x) \subseteq S$"?
Apr
2
revised Fastest way to meet, without communication, on a sphere?
added 798 characters in body
Apr
1
answered Fastest way to meet, without communication, on a sphere?
Apr
1
comment Fastest way to meet, without communication, on a sphere?
"**While you can determine your position relatively, you are on a sphere in a galaxy so far away that you cannot determine absolute 'north', 'south' etc. by the stars.": If the planet is rotating, you don't need a familiar sky to identify the poles. There's no way to choose North and South, but narrowing it down to two points is not bad.
Apr
1
comment Fastest way to meet, without communication, on a sphere?
Rotation (around the axis and around the sun) can be factored out if you have enough computational resources. This is the strategy I would choose if I was writing a story (or if it should actually happen to me): Go stand directly below the brightest fixed star (i.e. not planet on moon) in the firmament.
Sep
26
revised Sampling from Cartesian product without replacement, but with balanced totals
Added alternative formulation
Sep
26
revised Sampling from Cartesian product without replacement, but with balanced totals
Added alternative formulation
Sep
26
revised Sampling from Cartesian product without replacement, but with balanced totals
edited tags
Sep
25
revised Sampling from Cartesian product without replacement, but with balanced totals
edited body
Sep
25
awarded  Student
Sep
25
comment Identification of matrix index notation
I'm guessing the star is there in order to visually separate $a_i$, the array for a particular chemical element, from the indices $j$ and $k$? But this still doesn't explain the parentheses on $(j)$, so who knows...
Sep
25
revised Sampling from Cartesian product without replacement, but with balanced totals
added 113 characters in body
Sep
25
asked Sampling from Cartesian product without replacement, but with balanced totals
Mar
31
revised Continuous function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
added 155 characters in body
Mar
31
revised Continuous function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
added 105 characters in body
Mar
18
revised Is $\{x\}$ an element of $\{x,\{x,y\}\}$ or not?
added 133 characters in body
Mar
18
answered Is $\{x\}$ an element of $\{x,\{x,y\}\}$ or not?
Feb
26
awarded  Yearling
Feb
2
comment Coin flipping probability game ; 7 flips vs 8 flips
I'm surprised you think they're the same. "ties are discounted" changes the rules too much for my comfort, what can I say. JimmyHe's answer is very different: At a higher level, and more elegant, I must say-- but only if the core assertions are demonstrated, and I'm among those who don't find them self-evident.