[AnimalMuppet]

1-3: You can define a (mathematical) real number that cannot be interpreted as a position in the universe that can be physically realized, taking the Planck Length into account.

4: At the precision of the Planck Length, you have two integers that are the closest physically-meaningful values whose ratio approximates pi.

In both cases, you're confusing mathematical abstractions with what is physically realizable in a discrete system. You can't (meaningfully) do that.

[tossaway322]

The article unfortunately does not address the question of whether current mathematical analysis is an appropriate framework for a description of space/time. We are, in the end, dealing with elements "smaller than" (if that's the right phrase!) the Planck length. Of course, you can choose to ignore that and use what's already been provided, but to do so is "whistling past the graveyard". This has ramifications for all of string theory, quantum gravity et al.