Axiom of Infinity
Physical Reality of such a set
Many mathematicians and philosophers take issue with this axiom applying to the physical world, asserting that the world and human reasoning are finite in nature--therefore nothing infinite exists.
Christians qualify this statement further by stating that God is infinite, as are all things associated with Him (His Might, His Forgiveness, etc), but our finite minds cannot comprehend them. For this further reason we should not include infinite sets into our mathematical universe.