3 ms·
0.999
- Someone 7y agoThis is mathematics, so the rules are whatever you make them, as long as they are internally consistent. You can claim that 0.9 ̅ is a number that’s larger than every other number smaller than 1, yet smaller than 1, but then, you’ll face questions such as “what’s the average of 0.9 ̅ and 1?”. If you want averages to exist, you’ll have to break the rule the average of two numbers lies between them. So, the easiest way out of this is to say “in my version of math, we don’t do division”. I don’t even know whether ”0.9 ̅ is a number that’s larger than every other number smaller than 1, yet smaller than 1” can lead to a consistent system, but, as an example, in nimber theory, the nimber called ‘star’ is confused with zero: it is smaller than every positive nimber and larger than every negative nimber, but not equal to zero (https://en.m.wikipedia.org/wiki/Star_(game_theory) https://en.m.wikipedia.org/wiki/Star_(game_theory) )