/sci/ - Science & Math

>>12178354
Given a set [math]A[/math], let [math]\phi_A(x)=x\in A[/math].
(Conversely, given [math]\phi[/math], use class notation [math]A_\phi=\{x\mid \phi(x)\}[/math].)

Writing
[math]\forall (x\in A). \psi(x)[/math]
is just notation
[math]\forall x. x\in A\implies\psi(x)[/math]
which, with the above, we may write as
[math]\forall x. \phi_A(x)\implies\psi(x)[/math]

The defining property for the empty set is the one that is false for any x:
[math] \phi_{\{\}}(x)=\bot [/math]
So it appears the vacuous truth notion in this bounded context derives from Explosion.

>>12116863
Yeah I figured, but I think I proposed a solution: The chance for a player being at distance x after n steps is given by the symmetric function centered at n/2 given by the n-times convolution of a box with itself. You can do the convolution analytically, but I don't have it in my head. The expectation will be at the center. The player you is one step ahead is expected to be 1/2 ahead.

>>11633784
I was mostly thinking of a collaborative TeX file.
Also because I'd like to do something like that, given I'm on vacation now.

>>11564245
good, good

meta:
Those threads are now at 10-15 posts per hour, this is a bit too fast imho.
You guys think a /mg/ every second day is good?