Zero length. Uncountably infinite points.
You removed everything measurable.
What remains cannot be counted, only described by position.
Scholze and Clausen built all continuous mathematics from this dust.
Every smooth curve. Every topological space. Every surface you can imagine.
The foundation is not a line. It is the residue of infinite removal.
Cantor Set — Iteration 0
The interval [0, 1]. Everything.
Remove the middle third. Repeat. Infinitely.
Segments: 1 |
Total length: 1.000000 |
Each segment: 1.000000