there is a smallest integer which has never been named or seen by any human or machine
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Is -inf an integer for you ? (that's why you didn't ask about a floating point number, right ? As IEEE754 mandates the existence of such numbers...)
even if it is an integer I have no clue how you could think it would pass the rest of the definition
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Well my reasoning was: you can't pronounce it, only a symbol for that number (well, it's not a "true" number of course) and you can't see its "value" either. Of course, this is utterly flawed because the infinity doesn't make any sense as a number, and this was more of a joke ;)
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