I have 237474 ..... that number should be found within the set of natural numbers no? because if we say that the set of natural numbers has infinite elements, therefore that number should be found in the set. if that is not the case then what set is it in?
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5Welcome to Mathematics Stack Exchange. The set of natural numbers has infinitely many elements, but the elements themselves are finite – J. W. Tanner Dec 10 '19 at 04:00
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2If the digits extend infinitely to the left, then you get $p$-adic integers. But these are not natural numbers. – mr_e_man Dec 10 '19 at 05:10
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Does that means that the number is not an integer ? – Cooper Dec 10 '19 at 05:44
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@IsraelRamirez It's not that 'the number is not an integer' ... but that the 'infinite string of digits is not a number' – Bram28 Dec 10 '19 at 12:57
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No, that does not follow. There are infinitely many natural numbers, but the decimal representation of each natural number is only a finitely long string of digits.
An infinite string of digits would be in the set of .... strings of digits.
Bram28
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