VITALI SET CONSTRUCTION
STEP 1 / 15
The Real Line [0,1]
Starting point
We begin with the unit interval [0,1] — a seemingly well-behaved set of real numbers. Every subset should have a 'size' (measure), right?
FORMAL
m([0,1]) = 1
⚠ PARADOX
The assumption that every subset of [0,1] has a well-defined Lebesgue measure leads to contradiction.
Non-measurable sets · Axiom of Choice · rotates daily