I know the Arithmetic proof and everything but how to explain this practically to a kid who just started understanding the numbers?
In: 3202
To clear up some misunderstanding, it is important to know that with such infinite notations, we are really looking at limits; 0.99999…. is really a limit of the sequence 0.9, 0.99, 0.999,….,
that is: 0.99999… = lim_{n to infty} sum_{i=1}^n (9/(10^i)) ([notation](https://www.wolframalpha.com/input?i=lim_%7Bn+%5Cto+%5Cinfty%7D+%5Csum_%7Bi%3D1%7D%5En+%289%2F%2810%5Ei%29%29))
the sequence itself contains no entries which are 1, but the limit doesnt have to be in the sequence
at every added decimal, the difference to 1 shrinks by a factor of 10, this is convergence, so the limit, being 0.999… can only be exactly 1
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