Re: Well Ordering the Reals

David R Tribble said:
> David R Tribble said:
> >> These two sums are exactly the same, for instance:
> >> x = 1 + 1 + 1 + 1 + ...
> >> y = 1 + 2 + 4 + 8 + ...
> >
>
> Tony Orlow wrote:
> >> No, they are not. If they have the same number of terms, and every term in y is
> >> greater than its corresponding term in x (except the equal first terms), then y
> >> is celarly a larger quantity than x.
> >
>
> David R Tribble said:
> >> Same number of terms. How many is that?
> >
>
> Tony Orlow wrote:
> > Try N, the number of naturals and the length of the real line. It really
> > doesn't matter. If the number of terms is the same, y>x. When you claim they
> > are the same, the argument is vacuous, depending on total disregard for any
> > correspondence between terms.
>
> So "bijecting" the terms, i.e., finding a one-to-one correspondence
> between them, proves that the two sums have the same number of
> terms. But you said that bijections don't prove set sizes are equal.
>
> So how do we know the two sums have the same number of terms?
>
> Or have you changed your mind about bijections?
>
>

I am saying that if you assume they have the same number of terms, then y is
clearly larger, such that if |x|=N, then |y|=2^N-1. If you assume that the sum
is the same, then if the number of terms in y is N, then the number of terms in
x is 2^N-1. It's as simple as that. You do not simultaneously have the same
number of terms AND the same sum, and caliming so is patently false. Is that
really what you claim, that given the same number of terms the sum is the same?
That's mathematical insanity.
--
Smiles,

Tony
.

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