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From: Richard Damon <richard@damon-family.org>
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Subject: =?UTF-8?Q?Re=3A_Analysis_of_Flibble=E2=80=99s_Latest=3A_Detecting_v?=
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Date: Fri, 23 May 2025 12:01:55 -0400
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On 5/23/25 8:43 AM, Ben Bacarisse wrote:
> Richard Heathfield <rjh@cpax.org.uk> writes:
> 
>> On 21/05/2025 18:47, olcott wrote:
> ...
>>> *PAY ATTENTION*
>>> I am saying that a key element of the halting problem
>>> proof cannot exist, thus the proof itself cannot exist.
>>
>> Yes, it can, and it does.
> 
> You'd think that at some point in decades he's wasted on this he might
> have considered looking at the proofs that are not by contradiction.
> I've repeatedly suggested looking at Radó's Busy Bee problem and proof.

But that would require him to actually THINK and look for truth.

> 
>> Watch.
>>
>> Definition: a prime number is an integer >= 2 with no divisors >= 2 except
>> itself.
>>
>> Hypothesis: there is no largest prime number.
>>
>> Proof:
>>
>> Assume that a largest prime number Pn exists.
>>
>> Itemise all the prime numbers from P1(=2) up to Pn :
>>
>> P1 P2 P3 ... Pn
>>
>> Insert x symbols all the way along.
>>
>> P1 x P2 x P3 ... x Pn
>>
>> Add 1.
>>
>> The number thus calculated is not divisible by any prime in our list (there
>> being a remainder of 1 in each case), so the number calculated is (a)
>> prime, and (b) larger than Pn. Thus Pn is not the largest prime. This
>> contradicts the assumption made at the beginning, which must therefore be
>> false. Proof by contradiction.
>>
>> The proof that no largest prime exists despite its assumption that such a
>> prime /does/ exist - an assumption that turns out to be false.
> 
> Interestingly (and not, I think, coincidentally) Euclid's proof is not a
> proof by contradiction.  It shows (by case analysis) that any finite
> list of primes is incomplete.  There is (in the way Euclid does it) no
> need to assume anything (other than some basic axioms).
> 
> The same strategy can be used for the halting theorem.  The more direct
> proof essentially shows that the infinite list of Turing machines (there
> is only one, once we agree a numbering) does not include a halt decider
> (just like it does not include uncountably many other deciders that the
> cranks are never interested in).
> 
> PO seems to like talking to you so you might consider avoiding any
> arguments about contradictions by providing an outline of the direct
> proof instead.
> 
> I've lost count of the times when the proof by contradiction leads
> students astray.  Even if they don't think it's invalid, every year one
> has to counter the idea that all the decider has to do is "spot the
> tricky input" and the decider will work on everything else.
> 
>> I'm finding it hard to believe that you can really be this stupid. Perhaps
>> you just get off yanking people's chains.
> 
> Hmm...  Don't forget Hanlon's razor.  As for data points, PO has
> published a website whose purpose is to "bring new scripture to the
> world" and he has claimed, in a court of law, to be God.
> 
> Incidentally, there is even a modern proof by construction of the
> infinitude of the primes.  The idea being that since n and (n+1) have no
> prime factors in common, n(n+1) has more distinct prime factors that n.
> This gives a chain of ever larger sets of primes: the unique prime
> factors of 2x3, 6x7, 42x43 and so on.
>