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Zeno's paradoxes
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (ca. 490–430 BC) to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion . It is usually assumed, based on Plato's Parmenides 128c-d, that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides's view. Thus Zeno can be interpreted as saying that to assume there is plurality is even more absurd than assuming there is only "the One". ( Parmenides 128d).
Banach–Tarski paradox
Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original? The Banach–Tarski paradox is a theorem in set-theoretic geometry which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of non-overlapping pieces ( i.e. , subsets ), which can then be put back together in a different way to yield two identical copies of the original ball.2 April 2013 - Nature Detectors zero in on Earth's heat 2 April 2013 - Telegraph.co.uk Cern begins LHC upgrade to boost dark matter search
