[pjbeam]

The issue there I think is the idea of two reals having a "between."

[seanhunter]

Any two real numbers x and y are either equal or have an infinite number of reals between them don’t they? If your real numbers are x and y, then (x+y)/2 for example. The density of the rationals in the reals means that one of the numbers between them is provably a rational number.

[pjbeam]

For sure, I meant something more like a slot with a name.