Kinda wonder how a sphere of all things can possibly be modelled? I even heard you can like cut a sphere in half and axiomatically retain or conserve the prexisting volume or something to that effect. Like you could tangibly split it in two and conceptually still have >= prexisting volume or something? It seems absurd but I’m sure someone can hand-wave or radically justify exactly that somehow
Thank you so much for naming this seemingly crazy conjecture for me. Heard about it so vaguely forever ago and it seemed nuts but nice to finally to more (in)formally get to investigate it
I am surprised that nobody pointed out that there is a mathematical structure where you can divide by zero, the wheel:
https://en.wikipedia.org/wiki/Wheel_theory?wprov=sfla1
Kinda wonder how a sphere of all things can possibly be modelled? I even heard you can like cut a sphere in half and axiomatically retain or conserve the prexisting volume or something to that effect. Like you could tangibly split it in two and conceptually still have >= prexisting volume or something? It seems absurd but I’m sure someone can hand-wave or radically justify exactly that somehow
There’s a veritasium or vsauce video on that.
Can you link to that? I have zero idea how to intelligibly find a result to this inline with what you’re suggesting
I believe it is the Vsauce video titled The Banach-Tarski Paradox.
Thank you so much for naming this seemingly crazy conjecture for me. Heard about it so vaguely forever ago and it seemed nuts but nice to finally to more (in)formally get to investigate it