It does happen to some of us once in a while... Thinking on a Monday. In this case inspired by Sam Alexander on his Blog entitled "Infinitely Large vs. Arbitrarily Large"
[ http://www.xamuel.com/arbitrary-and-infinity/ ]
Now what caught my attention was the reference: "There is no individual number whose size (value) is infinity". (Sam Alexander) So, if infinity has no size, or that there can be no determinable value assigned to it...
How do we know that it exists? How can we then determine (mathematically) that there is infinity?
That, of course, in relation to the Universe, or even the Dark Matter within the Universe, would present a bit of a conundrum. Or, is it that what we observe is really an observation into our own infinity?
Not to change the subject, as Sam Alexander seems to think it is in the same context... ("Sets within Sets") is "ZFC, the Axiom of Foundation". Now wouldn't that be a Mandelbrot Set? The Basis of Fractals? Actually making infinity visible in spite of it being indeterminable. Or at least the possibility of doing so.
All in all an excellent Blog post Mr. Alexander. You made me think a bit. -d