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Why can't we apply Cantor's diagonal slash argument

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Why can't we apply Cantor's diagonal slash argument to the integers?
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File: ss+(2017-06-03+at+07.45.26).png (49KB, 751x462px) Image search: [Google]
ss+(2017-06-03+at+07.45.26).png
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>>8954603

So the positional numeral system can represent more integers than actually exist? An infinite random string of digits 0-9 would not be an actual integer? Spooky.
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>>8954630

What meaning can we give to these numbers?
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