On 23 Nov., 20:54, William Hughes <wpihug...@gmail.com> wrote:
> Well, looks like communication > has come to a halt. > > You are correct, if analysis requires > that oo be described by digits > then there is a contradiction in mathematics. > I see no way of convincing you that oo > cannot be expressed by digits, nor have > you given any evidence other > that vague handwaving that it can.
Clear mathematical formulas are not handwaving.
An analytical expression of infinity is this Limit[n-->oo] SUM[k=0 to n] a_k*10^k = oo
An expression by digits means nothing but leaving the powers of 10 aside and writing from right to left, i.e., the abbreviation ..., a_k, ..., a_3, a_2, a_1, a_0 where for every k there exists a digit a_(k+m) =/= 0, with m in |N.
This gives abbreviations like oo = ...111 = ...999 However, like sin(0) = sin(2pi) = sin(4pi) = 0 = 0+0 there is no problem with multi representation.
in any case the limit of my sequence > > 01. > > 0.1 > > 010.1 > > 01.01 > > 0101.01 > > 010.101 > > 01010.101 > > 0101.0101 > > ... has infinitely many digits right to the point as well as left to the point.
So it is incorrect to say that communication has come to a halt but it is correct to say that you have no further arguments to defend your position but do not want to admit that for reasons that I don't know.