I remember when this was introduced to us at school. The teacher started with
1/9 = 0.1 periodic.
2/9 = 0.2 periodic
and so on. Finally he wrote
9/9 and one pupil said instantly 0.9 periodic and I started to laugh because I saw this coming ;)
The problem with this is because we don't really understand infinity. The difference between 1 and 0.9 periodic in infinitely small which leads to zero but still we think we can stop this infite numbers at one point, subtract it from 1 and get the difference but then it's not periodic anymore and especially not infinite anymore. This is where mathematicians just define 0.9 periodic to be 1 - to get rid of this brainfuck ;)
Another brainfuck are real numbers in general:
between 0 and 0.1 are infinite numbers which is almost the same matter as with 0.9 periodic is 1.
