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Infinity has long been a contentious issue in mathematics, and in philosophy. Does it exist? How can we know? What about our computers, that only work with finite objects and procedures? Doesn't mathematics require infinite sets to establish analysis? What about different approaches to the philosophy of mathematics--can they guide us? In this friendly debate, Prof James Franklin and A/Prof Norman Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW, debate the question of `infinity' in mathematics.