Re: Cantor Diagonal Proof

On 11/04/2025 12:52, wij wrote:

On Fri, 2025-04-11 at 04:21 -0700, Keith Thompson wrote:

<snip>

Keep the insults to yourself.  Last warning.

 I still think 'nut' is a common word,

Lots of insulting words are common. That doesn't stop them from being insulting.

at least a terse word for people saying
one thing and doing the other (or a liar more appropriate?)

Calling your opponents' honesty into question doesn't hurt their credibility. It hurts yours.
I've been reading Keith's Usenet articles for a quarter-century and more, and in all that time he hasn't once posted anything that can even remotely be construed as being intended to deceive. To so casually impugn a man's integrity suggests strongly that you don't hold integrity in high regard, and that in turn leads me to think that maybe you don't value your own?
Nor, it seems, do you hold mathematics in high regard. Why else would you make such a ridiculous assertion, and attempt not to defend it (which you have singularly failed to do) but to insult those who show you the glaringly obvious proofs that you are wrong?
It's almost as if you're trying to get your opponents to plonk you so that they'll stop arguing against your ridiculous claim.
<snip>

Is this a lie? I have always consistently claiming "repeating decimals are irrational".

That you have made the claim is not in dispute. The claim itself is erroneous and easily disproved, but whether you believe it yourself is hard to establish, so I can't categorically label it a lie. It /might/ be a lie, or it might just be that you are extraordinarily bad at mathematics.
<snip>

Would, say "0.333<∞>" be clearer?  Could you agree that that refers to
the limit and gives a result that's exactly 1/3?

 0.333... approaches 1/3 --> no problem.
0.333... equals exactly to 1/3 --> no way (I have provided proofs and you don't).

The proof is simple, it has already been posted, and you have already decided that it can't be right because it proves you wrong.

If so, why do you
object to "..." but not to "<∞>" as a symbol for the limit?  (Note that
"..." is easier to type, unless you happen to have an ∞ key your
keyboard.)

 Who say I object the use of "..."?

You do, when you claim that 0.333... is irrational and that it sums to anything other than one third.
Do the math.
3)1.0000000000000...
If (as you seem to accept) 1/3 is rational, and if recurring decimals are irrational, 1/3's decimal expansion must be non-recurring. Great! Bring it on. I'll wait...

As said, it is 'the limit', not exactly equal (as explained)

At the limit, it becomes exactly equal (as explained).

As usual, you still only have irrelevant garbage talk, no valid logic proof.

Projection.
Keith's observations have been lucid and relevant. Yours have been more reminiscent of a crank riding a hobby.

If so, I can choose to stop responding.

Good plan. But if you do decide to continue, you might want first to think about why you post to Usenet. If your intent is merely to lead everyone to think you're an asshole, well, okay, it's working. But if you're looking for meaningful discussions with intelligent people, why drive your audience away with adolescent posturing? If you keep going the way you are, you'll end up spitting bile into the void because you've managed to crawl into everybody's killfiles.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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