Forget about triangles and voxels

https://www.alanzucconi.com/2016/07/01/signed-distance-functions/

Unless your 3d engine supports infinite resolution, you're a loser.

>>12

Not sure why it's separate when that was the entirety of my point.

It's separate from the completeness problem from >>9 that it was posted as replying to. Both problems -- lack of completeness and "fixed lower bound" -- lead, through different routes, to the same result: inability to take commonly needed limits.

Maybe you're are confusing infinite resolution with infinite bounds

1. The distance between any two points in a metric space is finite, because the distance function is defined from the product SxS with values in the nonnegative reals, so a volume is either unbounded or its bounds are automatically finite.
2. "Infinite resolution" on the distance function is precisely what is mandatory for convergence to work as expected, and what "having a fixed lower bound on distance, e.g. Planck length >>10" prevents.

since the universe itself is discrete.

And as soon as you present your mathematically consistent proof of this to the larger scientific community, your Nobel prize is a foregone conclusion.