Is $1234567891011121314151617181920212223......$ an integer? This question came from that one and from that talk where it's noted that "integers have a finite count of digits", so that the "number" in the title is not at all a number (not integer nor rational or real) . This statement seems to me justified because I suspect that if we admit an infinite count of digits we build a set of "numbers" that is not countable (but I've not a proof). I'm wrong?

Reading comments and answers I'm a bit confused. So I add a more specific question:
Is the string in the title a number in some model of Peano Axioms?

It is exactly the same thing as asking whether infinity an integer. But integer MUST have a finite number of digits. (the number in that title is "BOGUS")
