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Do infinite sets exist? Most mathematicians say yes, but to me it seems like infinite sets can only exist if we use inductive reasoning but not deductive reasoning. For example, in the set {1,2,3,4,...} we can't prove that the ... really means what we want it to. No one has shown that the universe doesn't implode before certain large enough "numbers" are ever glimpsed, so how can we say they exist as part of an "object" like a set. We can only do this by assuming the existence of the rest of the set since that seems logical base on our experience. But that seems like a rather weak argument.

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