On 23 Nov., 22:37, Virgil <vir...@ligriv.com> wrote:
> Analysis can show that the limit VALUE is oo in the extended reals, but > does not presume to claim that there is a decimal, or any other place > value based numeral, representing that limit value.
If the limit value Limit[n-->oo] SUM[k=0 to n] a_k*10^k = oo is accepted in the extended reals, then it is simply ridiculous to claim that the abbreviation ..., a_k, ..., a_3, a_2, a_1, a_0 is not in the abbreviations of the extended reals.
But William had agreed: "On the contrary, the fact that the analytic *limit* cannot be described in terms of digits is the point."
And he stated proudly:
Analysis: limit in real numbers: unbounded (oo in extended reals) limit of set of 1's: not estimated
Set Theory limit in real numbers: not estimated limit of set of 1's: {}
Therefore he would have to confess now that there is a contradiction between set theory and analysis. On the other hand we know the first commandment of matheology:
There's no con- tra-dic-tion! There's no con- tra-dic-tion! There's no con- tra-dic-tion! ...
