Abstract:
A paradox is, generally speaking, a disproof of our intuitive sense of what “should” be true. Through the ages, then, there have been many instructive and interesting paradoxes that have informed and reshaped mathematical intuition. As the field of mathematics has become more rigorous and less na¨ıve, the consequences of this increasing emphasis on logical precision have often escaped mathematicians. In this article, we will look at two famous paradoxes: Russell’s Paradox and the paradox of Banach and Tarski. These are two of the realizations that have shaped the world of mathematics in which we live and work: it is a weirder one than the layman might realize.
