Thread is huge.
Well I think an easy way to visualize it is that 0.9999.... represents the end of the 0. ..... cycle and 1 represents the beginning of the next 1. ..... cycle.
The exact end of a cycle and the beginning of the cycle are the same, e.g 2400hrs and 0000hrs are the same. The only way to represent the end of the 0. ... like the 2400hr case is 0.9999..., there is no other way to write it.
Just think about it as 0.9999... means that all the decimal places for the 0. .... cycle are filled ( hence the infinite 9's, and adding a 0.000....001 anywhere will give you something greater than 1). So it's the end of the 0.... cycle, and the beginning of the 1. ..... cycle. It's the same thing.
Edit: oops I think I made it sound more complicated..... ah well
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