On 23 Nov., 19:51, William Hughes <wpihug...@gmail.com> wrote: > On Nov 23, 2:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 23 Nov., 19:12, William Hughes <wpihug...@gmail.com> wrote: > > > It's still Piffle to say > > > > Analysis infers from the limit the number of required digits > > > It is obvious that you don't like analysis. Try to understand the > > function called logarithm with base 10. The number of digits is [lgx] > > + 1. > > Saying oo has an infinite number of digits is nonsense
It is not nonsense since set theory has "improved" analysis.
> (even though saying log_10(oo)+1 = oo is not nonsense).
Correct. And moreover we know that [lgx] + 1 gives the number of digits of x. Limit[n-->oo] SUM[k=0 to n] a_k*10^k = oo. The set { a_k | k in |N } has cardinality aleph_0.
> Your claim that oo requires digits is Piffle.
I do not say that oo requires digits. But oo can be expressed by digits. And to say that there are aleph_0 digits required is not nonsense as long as there are people who believe in the existence of infinitely many elements of |N.
But may you believe it or not: Can you imagine to admit a contradiction of set theory and mathematics, if it could be proven that analysis shows the existence of infinitely many digits left to the point in the limit of my sequence?
