| Cosmology is the only context in which it seems possible for an infinite set to be physically realized. The idea of an infinite universe has long been contemplated and for some time been modeled mathematically, but experimental evidence in favor of such a possibility would seem to be beyond reach. This, however, may not be so. The current dominant paradigm for the early universe, inflation, is both strongly suggested observationally and involves dynamics that may well entail a universe that is infinite at several levels. In this talk I will discuss the steps that have led us to this point, mention how future observations might actually give strong evidence of an infinite universe, and discuss both problems and interesting new perspectives that an infinite universe poses. |