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Re:0.999...= 1 by tomtomtom1 on Tuesday April 28, 2020 @05:08AM (#23005132)
but the long division algorithm never terminates.

why would it terminate at countable infinity?

Re:0.999...= 1 by recursive on Tuesday April 28, 2020 @10:07AM (#23007087)
You can show that the long division algorithm is looping. Further, you can show that it will continue, for these inputs, to produce `3`s forever with no change in state. How could `...` be defined such that it wasn't 0.333...?