Re: Cantor Confusion

On 16 Mrz., 21:18, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1174054064.244699.153...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,


The function of all cross sections, f: n |--> 2^n, is "continuous" in
the sense that never a jump by more than a factor 2 can occur because
the nodes of the tree are connected by an untearable network.

Following WM's argument, g:n |--> n is even more continuous in that it
can never "jump" by a difference of more than 1, so can never become
infinite at all.

It does never "become" infinite. This function "is" infinite, i.e., n
is always finite but not bounded.

The
domain is the same as the range, namely N.

The range of f: n |--> 2^n can never be the same as the domain, unless
both are empty.

That is fact, not by claim
but by construction of the tree. That's why I constructed it.

A construction which requires N for both the domain and range of
f: n |--> 2^n is fatally flawed.

You need only consider the number of pairs of parentheses and of unit
fractions per pair of parentheses in the proof by Oresme.

Regards, WM

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