On 2/26/2025 8:41 PM, Alan Grayson wrote:
Yes and yes. If the universe is infinite then the ratio of its
size to that of any finite subset is infinite, no matter how large
or small the subset is. Imagine the infinite set of the
integers. Consider the finite subset
{0,1,2,3,4,5,6,7,8,9,10,...,1e12}. It's size is obviously 1e12.
Now shrink the universe by striking every tenth number. Your
subset is now {0,1,2,3,4,5,6,7,8,9,11,...,1e12-1} and it's size is
1e12-1. But the universe is still infinite.
Brentc
I know enough about set theory to have easily generated what you write
above. But math isn't physics. If the finite observable universe
converges to a singularity, we have a hypothetical universe which is
not physically possible, whether finite or infinite. So I am not sure
how we can distingush between an infinite and finite universe. Set
theory does not help. AG
If you can grasp that, why can't you grasp Cantor's theory of infinite
sets. I and others have said over and over that the singularity is a
prediction of GR which assumes spacetime is a continuum. Quantum
mechanics almost certainly modifies the physics short of infinite density.
Brent
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