h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I've long had a problem with the way this argument is used to demonstrate the non-countability of the reals. I believe the canonical version of the argument is circular. (I don't reject the existence of reals - I'm happy with various proofs not based on Cantor's diagonal. I'm also not rejecting Cantor's diagonal slash, I just believe that its correct use effectively mandates that you already understand the issues of countability to a high level of sophistication. In effect you need to accept that the reals are not countable, which makes use of the argument as a means of demonstrating their non-countability an interesting diversion, but not a proof.)

I've written an article on this: http://www.h2g2.com/A386787 and would be interested to know what you think about this, because I've had this argument loads of times, and the argument in that article is the current state of my rebuttal of the 'party line'. (My argument is a little more subtle than it used to be, but I believe the fundamental objection is sound. The main difference between this and the last time I had this argument is that I now try to make it very clear that I don't reject result of the 'proof', just that I reject the notion that this is a proof. In the past people appear to have thought that I just didn't beleive in the reals...)

Hi!

Just to let you know that I've read your message. I haven't had time to read your article properly yet, but for the sake of completeness, I have added a link to your article at the end of mine.

I have to admit that although I understand what Cantor is saying, the question of whether it constitutes a 'proof' is an interesting one.

I'll get back to you later!

Regards, jd