[clooper]

Even if you increase the precision I can still generate a table T(P) for each fixed precision P. So the table is parametrized by P but it's still a table. The entire table T = colim T(P) is the colimit over all precision values but for every finite precision it is still a table.

[microtonal]

I did not say fixed precision. I said arbitrary precision, so P is infinite.

The only counter-argument is that even arbitrary precision is fixed-precision because computer memory is finite. But that's kind of a silly argument, because then you are arguing that computers can never reason, because they have finite memory, and moreover humans cannot reason either, because there is a finite number of brain cells.

[clooper]

P obviously can't be infinite, even in theory, if you want the computation to terminate.