5 ms·

Where is 1⁄3? Is it before or after (pi - 3)?

• phkahler 4y ago
  We need to switch to the scheme that converts name/description to an integer for that. If you mean the repeating decimal, I don't know if it's before or after pi because I can't identify (name) their locations. It's the same argument. If I can accept that there are more reals than reals with finite descriptions, why can't there be integers without finite descriptions/positions?
  • jacobmartin 4y ago
    > If I can accept that there are more reals than reals with finite descriptions, why can't there be integers without finite descriptions/positions? Because the integers are defined as the finite successors to the number 0 and their additive opposites. See, for instance, the construction section of: https://en.m.wikipedia.org/wiki/Integer https://en.m.wikipedia.org/wiki/Integer You can start talking about numbers that can't be constructed in this way, but then you've ceased to be talking about the integers.
    • phkahler 4y ago
      Is the size of the set of integers an integer?
      • jacobmartin 4y ago
        No, usually the cardinalities of infinite sets are represented by things called aleph numbers: https://en.m.wikipedia.org/wiki/Aleph_number https://en.m.wikipedia.org/wiki/Aleph_number. But it isn't, in any case, an integer.
        • phkahler 4y ago
          Thanks! That to me is the most useful response to my ramblings today!