On 1/30/23 10:21 AM, olcott wrote:
> On 1/30/2023 6:10 AM, Richard Damon wrote:
>> On 1/30/23 12:08 AM, olcott wrote:
>>> On 1/29/2023 8:52 PM, Richard Damon wrote:
>>>> On 1/29/23 9:27 PM, olcott wrote:
>>>>> On 1/29/2023 8:06 PM, Richard Damon wrote:
>>>>>> On 1/29/23 8:48 PM, olcott wrote:
>>>>>>> On 1/29/2023 7:41 PM, Richard Damon wrote:
>>>>>>>> On 1/29/23 8:28 PM, olcott wrote:
>>>>>>>>> On 1/29/2023 7:10 PM, Richard Damon wrote:
>>>>>>>>>> On 1/29/23 7:28 PM, olcott wrote:
>>>>>>>>>>> On 1/28/2023 9:47 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/28/23 4:29 PM, olcott wrote:
>>>>>>>>>>>>> On 1/28/2023 3:13 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/28/23 3:59 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/28/2023 2:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yes, you can build SOME Deciders from a Sumation.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Not All Deciders can be built from a Sumation.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> One TM is *ALL* deciders.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Really?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It can be both a is_prime and is_perfect decider?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Maybe your problem is you don't understand at all what a
>>>>>>>>>>>>>> decider is?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You just don't understand the basics of category theory,
>>>>>>>>>>>>>>>> and just fall into the fallacy of Proof by Example.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Just because one subset of a set happens to have a
>>>>>>>>>>>>>>>> property doesn't mean that property applies to the whole
>>>>>>>>>>>>>>>> class.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Try and provide a single counter-example where IS_SUM
>>>>>>>>>>>>>>> gets the wrong answer.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If the question is Is the number prime?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If there are no counter-examples that prove that IS_SUM
>>>>>>>>>>>>>>> gets the wrong
>>>>>>>>>>>>>>> answer then this logically entails that IS_SUM always
>>>>>>>>>>>>>>> gets the correct
>>>>>>>>>>>>>>> answer.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But only to the one question it was built for.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Likewise for DOES_HALT, there are zero countability issues
>>>>>>>>>>>>> with
>>>>>>>>>>>>> DOES_HALT. DOES_HALT merely needs to compute the mapping
>>>>>>>>>>>>> from any
>>>>>>>>>>>>> arbitrary input pair of finite strings to its accept or
>>>>>>>>>>>>> reject state.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Can you PROVE that this is doable?
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> We can change IS_SUM to allow any arbitrary finite set of
>>>>>>>>>>> finite string
>>>>>>>>>>> inputs. If any of these finite strings contains a character
>>>>>>>>>>> that is not
>>>>>>>>>>> an ASCII digit then IS_SUM rejects, otherwise IS_SUM is as it
>>>>>>>>>>> was
>>>>>>>>>>> previously specified.
>>>>>>>>>>
>>>>>>>>>> Ok, how do you use IS_SUM to answer the IS_PRIME question?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> IS_PRIME would have a single finite string of ASCII digits as
>>>>>>>>> its only input and you already know this is computable.
>>>>>>>>>
>>>>>>>>>> IS_SUM takes the countably infinite number of inputs
>>>>>>>>>
>>>>>>>>> IS_SUM takes a finite set of finite string inputs
>>>>>>>>> IS_SUM takes a finite set of finite string inputs
>>>>>>>>> IS_SUM takes a finite set of finite string inputs
>>>>>>>>> IS_SUM takes a finite set of finite string inputs
>>>>>>>>> IS_SUM takes a finite set of finite string inputs
>>>>>>>>
>>>>>>>> And computes ONE mapping, out of the uncountable infinte many
>>>>>>>> mappings of strings -> the set of answers for each input.
>>>>>>> IS_SUM need not ever count any uncountable set. All that IS_SUM
>>>>>>> must do is compute each mapping that it is presented with, one
>>>>>>> finite set of finite strings at a time.
>>>>>>>
>>>>>>
>>>>>>
>>>>>> So????
>>>>>>
>>>>>>
>>>>>> We aren't talking about IS_SUM being non-computable,
>>>>>
>>>>> Then the "you" of "we" is off topic. Countability was supposed to
>>>>> be an alternate proof that halting is undecidable.
>>>>>
>>>> Right, countablility of mappings.
>>>>
>>>> The computability of a single mapping show nothing about the
>>>> countability arguement.
>>>>
>>>> No one says that NO mappings are computable, just that most are not.
>>>>
>>>
>>> No one can show even one mapping of a finite set of string inputs to
>>> IS_SUM that is not computable, thus the conclusion that there are more
>>> than one counter-example is totally refuted.
>>
>> ????
>>
>> You seem to think that is_sum computes multiple mappings.
>>
>> *A* mapping, as being talked about here, is a complete listing of the
>> required output for every possible input.
>>
>> IS_SUM computes *ONE* mapping of input to output.
>>
>> Yes, it can computer the
>>
>>>
>>>> You clearly don't understand categorical logic.
>>>>
>>>
>>> Categorically exhaustive reasoning is my key innovation it utterly
>>> eliminates the error of omission.
>>
>> No, it is your key fallicy. You seem to think that a detail analysis
>> of one case tells you all you need about every case that you don't
>> look at.
>>
>> That is just
>>
>>
>>>
>>> If it is impossible to show as many as a single counter-example then we
>>> can correctly generalize this to say that more than one counter example
>>> also does not exist.
>>
>> No, you are just using the fallacy of the Red Herring, because you
>> demand a counter-example of something that isn't the problem.
>>
>
> If no counter example can be provided that a decision problem is
> undecidable then this proves that it is decidable.

I HAVE given couter examples, you are just too stupid to understand them;

Your problem is you are stuck in your Herring with Red sauce and are
forgetting what the actual problem is.

>
>> How does your "IS_SUM" machine answer both the question of "is 8 the
>> sum of two primes?" and "is 8 a perfect number?" (assuming the first
>> is what you are defininig IS_SUM to be, not sure what else you mean,
>> sometime it seems like IS_SUM is computing the sum of two numbers give
>> to is, which isn't an "IS" question.
>>
>
> IS_SUM determines if its first finite string of ASCII digits is the sum
> of its remaining finite list of finite strings of ASCII digits. Maybe
> you need to take notes. There is also an adaptation of IS_SUM that takes
> arbitrary finite strings.

I don't remember you ever defining IS_SUM, and that definition is one of
the most worthless deciders possible.

So, how can you use IS_SUM to compute the mapping of IS_PRIME.

>
>>
>> Note, these two question both take the SAME input (8), but have
>> different outputs,
>>
>> For IS_SUM_OF_PRIMES, the answer is yes, because 8 = 3 + 5
>>
>> For IS_PERFECT, the answer is no, because 8 has factors to 1, 2, 4
>> which only total to 7, not 8.
>>
>> You claim same machine, in is the same, output will be the same, thus
>> must give the wrong answer to one of them.
>
> One decision problem per TM. A finite number of different decision
> problems could be selected for computation by a single TM when the
> ordinal number of the decision problem is the first input parameter.

So, you totally don't understand the argument.

YES, one decision problem per TM

There are only a countable infinite number of TMs

There are an UNCOUNTABLE infinite number of decision problems.

Thus, not all decision problems can be computable.

>
> Every decision problem that operates on a finite set of finite strings
> is not uncomputable for any countability reasons.

How do you answ3er an uncountable number of problems with only a
countable number of machines?

You don't seem to understand the question, my guess is you are just too
stupid.

>
> The most straight forward to validate the Goldbach Conjecture is to
> simply test every element of the set of natural numbers. Since this is
> not a finite list of inputs it is not computable. Mathematical induction
> can be used to algorithmically compress the analysis of some infinite
> sets. https://www.britannica.com/science/Goldbach-conjecture
>

But you need to find an induction pattern that does compress it. Not all
infinte patterns can be shown with induction.

>>>
>>>
>>>> Again, your use of the fallacy of proof by example.
>>>
>>
>