On: 0.999...= 1

[tomtomtom1]

but the long division algorithm never terminates.

why would it terminate at countable infinity?

[recursive → tomtomtom1]

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...?