/sci/ - Science & Math

>>14954603
>i find Stable Diffusion images somewhat soulless
Yes.

>>12444730
The identity operator has a spectrum with one element and it isn't compact.

I was exceptionally lurking in /mg/ and now I'm curious about something.
>>12193159
If a compact set [math]A[/math] is strictly contained in the interior of a compact set [math]B[/math], then [math]A[/math]'s Lebesgue measure is strictly smaller than [math]B[/math]'s. The proof is simple, an element of [math]B[/math]'s interior that isn't in [math]A[/math] either has some neighborhood in [math]B[/math] with empty intersection with [math]A[/math] or it doesn't. If it doesn't it's naturally in [math]A[/math]'s closure, which contradicts the hypothesis. This open set nets us the strict inequality.
Because of that, the existence of such a sequence would imply that [math]\mathbb{R}^+[/math] has an uncountable, totally ordered (the fact that it's totally ordered is the essential point here) subset. I'm pretty sure that's impossible, but I'm going to sleep soon and the argument isn't coming to me.