Date: Dec 9, 2012 5:06 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 175
Matheology § 175

Until then, no one envisioned the possibility that infinities come in

different sizes, and moreover, mathematicians had no use for ?actual

infinity.? The arguments using infinity, including the Differential

Calculus of Newton and Leibniz, do not require the use of infinite

sets.

T. Jech: "Set Theory", Stanford Encyclopedia of Philosophy (2002)

http://plato.stanford.edu/entries/set-theory/

There are only countably many names.

An uncountable set of names cannot be well-ordered - because it does

not exist.

A set of numbers cannot be well-ordered unless all the numbers have

names.

This seems to contradict Cantor's diagonal argument - but only if

infinite set are complete.

Conclusion: Infinities do not come come in different sizes. In fact

mathematicians have never had use for actual infinity because they

could not. All they could is to believe that they had use for actual

infinity, i. e., for numbers that have no names and cannot be used.

That's called mathelogy.

Regards, WM