Infinity+1

When children play Superheroes and constantly try to one-up each other’s powers, it’s not unusual for them end up arguing over whether or not “infinity,” “infinity plus infinity,” and “infinity times infinity” are valid measures of super strength. While most people would look upon this exchange with a look of amusement, those two kids might be on to something a bit more sophisticated. This presentation is on Georg Cantor’s famous theorem which states that there is no greatest cardinal number of a set. That is, there cannot be a “biggest” collection of items in terms of how many items are in said collection, or set. This would imply that not only are there sets with an infinite number of items, and then other infinite sets with even more items, but if one were to construct a set which contained the number of how many items are in these increasingly infinite sets, this set would also be infinite. This presentation will explore and discuss this seemingly counter-intuitive fact of mathematics as well as take a look at some of the paradoxical statements which accompany this theorem, and the how and why these contradictions led mathematicians to reform set theory and bring about modern practices and axioms in set theory