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 Originally posted by radagast It depends on your definition of exists, I suppose. In a defined mental construct, such as the mathematics of real numbers, the proof of an infinite number of real numbers between the number 1.0 and 2.0 is a proof of the existence of an infinity, at least constrained to within that mathematical construct. Since common dictionary definitions of existence and exist do encompass mental constructs as well as external reality, I see this as proof of existence within the above given context. I do not say this says anything about external, objective reality.
Since infinity cannot be a concept, it cannot be a number, other then to state that 'one' of them exists.

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.