Re: Cantor Confusion

In article <1174139848.400476.4970@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

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.

Then lim n {n --> oo} = aleph_0 is false.

This function "is" infinite, i.e., 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.

There has been a long discussion of how to define functions. According
to EVERY definition considered in that discussion, the alleged function
described by WM as having domain and range equal to N and having
f: n |--> n^2, is NOT a function at all.

WM's ignorance of even the most primitive of mathematical ideas leads
him to make a fool of himself too often.
.