On a side note, our decimal system has the initially-weird consequence that 0.999… is well-defined, but 0.000…001 isn't. The reason for that is that while 0.999… is representable as an infinite series, 0.000…001 isn't—you can't keep adding anything to make the series continue, you have to keep multiplying (by 1/10). That make it unrepresentable as a decimal.
Incidentally, the infinite series 0/1 + 0/10 + 0/100 + 0/1,000 + 0/10,000 + ... isn't equal to 0. It's an infinite series, it doesn't equal anything. It does converge to 0, but it doesn't equal 0.
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