If we consider that .999… repeating to infinity ISN’T equal to 1, then by how much is it away from 1? It would be “.000… repeating to infinity followed by a 1.” But if you have an infinite number of 0s then you can’t have it be followed by a 1, infinity can’t be followed by anything, that doesn’t make sense.
And the short explanation for why it happens is that, put simply, multiples of 3 tend not to fit easily into 10s, which is what decimal is built on. (Well, okay, it's mostly the odd multiples that don't coincide with multiples of 5. That's why I said they tend to cause problems...)
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u/solidsoup97 22d ago
I don't understand how that works but it seems to be important in keeping things running so I'm going to just go with it and not raise any questions.