Web Site: https://www.victella.me

e-mail: email@victella.me

Victella©

The Personal Website of
Victor Vella

Site Last Updated:  16 May 2018

Victella Website

This website is intended to hold articles and other information that may be useful to some members of the public.  Currently, there is only one article.  However, the sub-website, ETAC, contains the details and download of a new programming language.

NOTE: This website is written in Australian English.

Articles

There is currently only one article to download.

The Collapse of Transfinite Cardinals

This is a free article of interest mainly to pure mathematicians.  The purpose of the article is to prove, rigorously, that the existence of transfinite cardinal numbers is untenable at this point in time because the traditional “proofs” of their existence are logically invalid.  The only transfinite cardinal number that may be admitted is À0.  The definition of transfinite cardinal numbers depends upon Cantor's theorem and the non-denumerability of the real numbers.  The “proofs” of those theorems depend upon Cantor's diagonal method.  The article proves that the diagonal method is self-contradictory, and consequently, the existence of transfinite cardinal numbers is untenable (except for À0).  The article does not prove, with certainty, that the transfinite cardinal numbers do not exist, but that they have not yet been validly proven to exist.  (Note that the word “exist” here has nothing to do with metaphysics; the word is a purely logical concept.)

To download the free article (The Collapse of Transfinite Cardinals), click the following link.

Download: The Collapse of Transfinite Cardinals (216 kB)

Websites

ETAC

This is the official sub-website for the ETAC programming language.