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by tom-thistime 2239 days ago
Ok. (a) I think you're saying that 0.00 ... 1 is not a real number. (b) Do we agree that lim n->inf 10^-n is a real number? (I.e. zero?) (c) Then you're saying that limit in "(b)" is not a reasonable definition of the string "0.00 ... 1". Is that correct?
1 comments

That is correct.

The limit of lim n->inf 10^-n is exactly 0, it is not 0.00...1.

Since we have no common definition of what 0.00...1 might possibly mean, let's say we agree.