Re: infinity

David R Tribble said:
> Tony Orlow (aeo6) wrote:
> > For a range n, the number of whole numbers in n is twice the number of even
> > numbers in n, even if n=N. To claim they are the same number, one has to give
> > the evens twice the range. This is why I am advocating the use of unit
> > infinities, because otherwise comparison is impossible.
>
> So given this hypothetical unit infinity, which is presumably what
> you've been calling N, we should be able to assert that:
> s = 1 + 1 + 1 + 1 + ...
> s = N
> and that s is a very large (the largest) whole number, right?
No, not the largest, and not the smallest infinity either. It's the most simple
in concept, and the easiest with whoch to form a bijection using counting
numbers.
>
> What then is the value of:
> t = 1 + 2 + 3 + 4 + ...
> t = ?
(N^2+N)/2. Draw a diagram"
x
xx
xxx
xxxx
xxxxx
........

Notic how it looks like half a square?

>
> t must be a whole number, since it's just the sum of whole numbers.
> But it's also obvious that t > s, so t > N, right?
Absolutely.
>
> I assume you're going to say that t is a larger infinity than N,
> even though they are both whole numbers in your world, and I
> though you've been saying all along than N is the largest whole
> number.
I don't think I ever said N was the largest whole number. It is simply a unit
infinity used to compare all others. By the way, there are smaller infinities
too, such as the sum of the harmonic series.
>
>

--
Smiles,

Tony
.

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