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It's because the rigorous mathematical definition is more subtle. It's defined as the smallest real number such that repeating this process (putting more 9's in
by jhanschoo 7y ago
It's because the rigorous mathematical definition is more subtle. It's defined as the smallest real number such that repeating this process (putting more 9's in the end) can't result in a number that's greater than it. So as long as you have a number that's smaller than 1, there's a gap there, and repeating the process of adding 9's will eventually give you a number that lies in that gap.
- vfinn 7y agoYeah, it makes sense if the whole foundation of mathematics is laid out in such way that the above has to be true (kinda circular, but still), and this would mean that what I'm talking about is actually not mathematics but something else :).