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> 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
by 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 agoIs the size of the set of integers an integer?
- jacobmartin 4y agoNo, 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 agoThanks! That to me is the most useful response to my ramblings today!