On 23 Nov., 13:27, William Hughes <wpihug...@gmail.com> wrote:
> So to summarize: > > Analysis: > limit in real numbers: unbounded > (oo in extended reals) > > limit of set of 1's: not estimated
Analysis says there are infinitely many 1's distinguished by their positions which are an abbreviation for the exponents of 10.
Remember: 111 = 1*10^0 + 1*10^1 + 1*10^2 ...111 = 1*10^0 + 1*10^1 + 1*10^2 + ... This is a sum over all natural numbers (and 0). Therefore the positions with 1's in the decimal representation are infinitely many (or aleph_0).
If this was disputed, then you could also dispute that the cardinality of |N is "estimated" as aleph_0.
> > Set Theory > limit in real numbers: not estimated > limit of set of 1's: {} > Contradiction: One - and that is sufficient. But if required I could present a lot more.
