BANACH-TARSKI PARADOX
step 1 of 5
1
The Sphere
Begin with a single solid sphere — say, an orange. It is composed of uncountably many points, each located by three coordinates. The sphere contains no gaps, no holes, no missing pieces. It is whole.
VISUALIZATION
One perfect sphere, resting in empty space. Every point accounted for. Nothing missing, nothing extra.
S = { (x,y,z) : x^2 + y^2 + z^2 <= 1 }