Comment by FilosofumRex
2 days ago
The field Qp of p-adic numbers is complete with respect to the p-adic norm, but is not ordered in the same sense as field of real numbers. It's still uncountable infinite. If there is a sense in which "gaps" or Holes can be introduced without breaking its completeness, that would make it very useful for modeling reality
p-adics may be useful, yes, as may other fields.
They do not constitute a field with a smallest non-zero element.