LibriumArcana.Games

I was messing around on mathematica, and apparently Int[x, Int[x, Int[x, Int[x, ..., 1], 1], 1], 1] = sqrt2 - 1. Is there a way to prove this? I assume that the notation Int[f,a,b] means integral of f from a to b. Let Ω = Int[x, Int[x, Int[x, Int[x, ..., 1], 1], 1], 1]; then Ω = Int[x,Ω,1] = 1/2 - ...

Okay. I was under the impression singularities must be pointlike. Is this example analogous to a singularity not at a point? f(x) = x^(1/2) has a singularity on (-\inf,0]. On (-\inf,0), surely. It's somewhat analogous, yes, but perhaps with some caveats. Although I suppose that to preserve mathemat...

That's what I meant: the universe in that scenario is infinite spatially, and contracts asymptotically toward infinite density; how can it be both infinite spatially and tend to singularity? I'm not quite certain what it is that you're asking. If the matter distribution is homogenous and the univer...

So, the density will accrue asymptotically? Of course. Start with a homegenous matter distribution, assume that gravitational force dominates over large distances, pick an arbitrary origin, and treat the rest of the universe as layers of spheres which will gravitationally contract toward the origin...

... Am I grasping that much at least? And if that is true, because this line of 'stuff' is equally proportional in both size and distance as an infinite quantity, and coupled with what Robert Walper said about Time being relative only within the universe itself, then the universe is currently of an...