Paradoxes of infinity

set of philosophical problems

theorem that there exists a decomposition of a unit solid ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the unit sphere

thought experiment proposed by David Hilbert

infinite surface of revolution with infinite surface area enclosing a finite volume, which contributed to 17th century debate on the nature of infinity

paradox involving a game with repeated coin flipping

not all numbers are squares, so all the numbers, including both squares and non-squares, must be more numerous than just the squares; yet, for every number there is exactly one square, so there cannot be more of one than of the other

philosophical puzzle that is a variation on Zeno's paradoxes