>>14585848
>1. Real numbers only have finite place values (...hundreds, tens, ones, tenths, hundreths...)
Are ordinal numbers real numbers? If not, then why not just define something analogous to ordinals that fits between any two expressions of real numbers? i.e.
>Note 0.0000...1 is not a number, because of rule 1
would be an invalid inference under such a construction, because rule 1 would only prove it to not be a real number.