Re: Well Ordering the Reals

David R Tribble said:
> Tony Orlow wrote:
> > You see, as far as I am concerned, there is no smallest infinite,
> > as one can subtract a finite, or divide by a finite, and get a smaller infinite
> > number, just like you say there is no largest finite. So, omega means nothing
> > to me. I deal with a unit infinity which I generally call N, which represents,
> > not some definite number, but the 1-1 correspondence between element count and
> > element value, 1 element per unit of value, across the infinite real line. It
> > can be thought of as the length of the infinite line, and the number of unit
> > segments and natural numbers in the line, but isn't really a particular number.
> > It's more of a variable which can take on infinite values.
>
> Now you are contradicting yourself. You have stated that 'N' is your
> "standard unit infinity", and that it is:
> N = 1 + 1 + 1 + 1 + ...
>
> This makes your 'N' a distinct NON-variable value.
> Or have you changed your mind about it?
>
>
Oh, does it? Precisely how many 1's are added in that infinite sum of 1's? A
specific number, or some infinite indefinite number? You say "aleph_0", but
what does that really mean? It's not an actual number, as you yuorself admit.
--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... David R Tribble said: ... > hyperintegers, not the reals in the unit interval. ... >> implicit infinite string of leading 0's which add no value to the sum, ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> David R Tribble wrote: ... >> Tony Orlow wrote: ... > bit positions to achieve the infinite values in *N. ...
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  • Re: infinity
    ... > David R Tribble said: ... >> Tony Orlow wrote: ... >>> possible difference is not infinite if no differences can possibly be ...
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  • Re: Well Ordering the Reals
    ... > David R Tribble said: ... >>> infinite number of bits. ... The entire bit string need not be. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... David R Tribble said: ... Tony Orlow wrote: ... So which n is that "infinite case"? ...
    (sci.math)