Re: Well Ordering the Reals

Virgil said:
<much spewage snipped>
> > > > Yes, and the bit string filling that uncountable space must be
> > > > expressible as a repeating pattern
>
> There are not enough repeating patterns, only countably many, and EVERY
> pattern must be allowable, repeating or not.
>
>
>

The T-riffic numbers are digital numbers with limit points that define
countable neighborhoods. The intervening strings between limit points, which
may be finite, countably infinite or uncountably infinite, are defined using
repeating patterns. So, the T-riffics can represent infinite values. But, you
are right, one cannot, say, represent pi*N, with its uncountably long non-
repeating bit string, without actually having an infinite string. For such
values, there is no T-riffic notation, but that's okay. The T-riffics don't
claim to be able to represent EVERY infinite value, but should be able to
represent infinite values expressed as simply algebraic formulas on N, which is
at least an improvement over adics.
--
Smiles,

Tony
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... >> There are not enough repeating patterns, only countably many, and EVERY ... > may be finite, countably infinite or uncountably infinite, are defined using ... the T-riffics can represent infinite values. ... > repeating bit string, without actually having an infinite string. ...
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  • Re: Well Ordering the Reals
    ... we could talk about how the infinite sum of the divergent ... The T-riffics probably solve all of them. ... it's funny how declaring bits at infinite positions in the string ... uncountably infinite sequentially ordered sets, ...
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