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computers / comp.ai.philosophy / The problem of not enough TM for every decision problem has been resolved

SubjectAuthor
* The problem of not enough TM for every decision problem has beenolcott
`* Re: The problem of not enough TM for every decision problem has beenRichard Damon
 `* Re: The problem of not enough TM for every decision problem has beenolcott
  `* Re: The problem of not enough TM for every decision problem has beenRichard Damon
   `* Re: The problem of not enough TM for every decision problem has beenolcott
    `* Re: The problem of not enough TM for every decision problem has beenRichard Damon
     `* Re: The problem of not enough TM for every decision problem has beenolcott
      `* Re: The problem of not enough TM for every decision problem has beenRichard Damon
       `* Re: The problem of not enough TM for every decision problem has beenolcott
        `* Re: The problem of not enough TM for every decision problem has beenRichard Damon
         `* Re: The problem of not enough TM for every decision problem has beenolcott
          `- Re: The problem of not enough TM for every decision problem has beenRichard Damon

1
The problem of not enough TM for every decision problem has been resolved

<tpc8tb$3i43g$1@dont-email.me>

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From: polco...@gmail.com (olcott)
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Subject: The problem of not enough TM for every decision problem has been
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 by: olcott - Sat, 7 Jan 2023 17:07 UTC

A UTM processes a subset of the set of finite strings such that
the first string TM description is concatenated to its input
forming the complete set of every TMD + INPUT combination.

All of the finite strings left over from the set of finite strings
are totally irrelevant because the complete set of decision problems
has already been specified.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: The problem of not enough TM for every decision problem has been resolved

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From: news.x.r...@xoxy.net (Richard Damon)
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The problem of not enough TM for every decision problem has been
resolved
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 by: Richard Damon - Sat, 7 Jan 2023 17:23 UTC

On 1/7/23 12:07 PM, olcott wrote:
> A UTM processes a subset of the set of finite strings such that
> the first string TM description is concatenated to its input
> forming the complete set of every TMD + INPUT combination.
>
> All of the finite strings left over from the set of finite strings
> are totally irrelevant because the complete set of decision problems
> has already been specified.
>
>

But the subset is just the same size as the set of finite strings since
they both are of size "countable infinity".

This is one of the "confusing" properties of countably infinite sets,
countably infinite proper subsets are still the same size as there
proper super set.

The problem is (if I am remembering right) that the number of decision
problems isn't a countably infinte number, but an uncountable infinite,
which IS larger than the number of finite strings that could be given to
a UTM, since that is, BY DEFINITION, countable.

Since you seem to have problems understanding the countable infinite, I
don't expect you to understand the uncountable infinite.

Re: The problem of not enough TM for every decision problem has been resolved

<tpcd3k$3ilth$1@dont-email.me>

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The problem of not enough TM for every decision problem has been
resolved
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 by: olcott - Sat, 7 Jan 2023 18:19 UTC

On 1/7/2023 11:23 AM, Richard Damon wrote:
> On 1/7/23 12:07 PM, olcott wrote:
>> A UTM processes a subset of the set of finite strings such that
>> the first string TM description is concatenated to its input
>> forming the complete set of every TMD + INPUT combination.
>>
>> All of the finite strings left over from the set of finite strings
>> are totally irrelevant because the complete set of decision problems
>> has already been specified.
>>
>>
>
> But the subset is just the same size as the set of finite strings since
> they both are of size "countable infinity".
>

Although it may be conventional to say it that way the set of finite
strings that are prepended with a valid TMD is a proper subset of the
set of all finite strings.

> This is one of the "confusing" properties of countably infinite sets,
> countably infinite proper subsets are still the same size as there
> proper super set.
>

If this means that conventional set theory claims that a proper subset
of a set is also an identical set to this set then conventional set
theory is wrong.

> The problem is (if I am remembering right) that the number of decision
> problems isn't a countably infinte number, but an uncountable infinite,
> which IS larger than the number of finite strings that could be given to
> a UTM, since that is, BY DEFINITION, countable.
>

Yes that is the mistake of conventional wisdom.
An infinite set of unique TMD's has each element of the unique set of
finite strings appended. A UTM processes each element of these TMD+INPUT
pairs.

> Since you seem to have problems understanding the countable infinite, I
> don't expect you to understand the uncountable infinite.

Reals are construed as uncountably infinite because there has previously
been no way to uniquely identify a pair of immediately adjacent points
on a number line. The assumption has always been that there is always a
point between two points thus no two points are immediately adjacent.

Using interval notation we can see that the line segment specified by
[0,1] is exactly one geometric point longer then the line segment
specified by [0,1). Thus the point at the right end of [0,1] is
immediately adjacent to point at the right end of [0,1) with no points
in-between.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: The problem of not enough TM for every decision problem has been resolved

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 by: Richard Damon - Sat, 7 Jan 2023 18:41 UTC

On 1/7/23 1:19 PM, olcott wrote:
> On 1/7/2023 11:23 AM, Richard Damon wrote:
>> On 1/7/23 12:07 PM, olcott wrote:
>>> A UTM processes a subset of the set of finite strings such that
>>> the first string TM description is concatenated to its input
>>> forming the complete set of every TMD + INPUT combination.
>>>
>>> All of the finite strings left over from the set of finite strings
>>> are totally irrelevant because the complete set of decision problems
>>> has already been specified.
>>>
>>>
>>
>> But the subset is just the same size as the set of finite strings
>> since they both are of size "countable infinity".
>>
>
> Although it may be conventional to say it that way the set of finite
> strings that are prepended with a valid TMD is a proper subset of the
> set of all finite strings.

But it is still just

>
>> This is one of the "confusing" properties of countably infinite sets,
>> countably infinite proper subsets are still the same size as there
>> proper super set.
>>
>
> If this means that conventional set theory claims that a proper subset
> of a set is also an identical set to this set then conventional set
> theory is wrong.
>

No, not identical, just the same size.

This is part of the confusing thing with infinite numbers.

>> The problem is (if I am remembering right) that the number of decision
>> problems isn't a countably infinte number, but an uncountable
>> infinite, which IS larger than the number of finite strings that could
>> be given to a UTM, since that is, BY DEFINITION, countable.
>>
>
> Yes that is the mistake of conventional wisdom.
> An infinite set of unique TMD's has each element of the unique set of
> finite strings appended. A UTM processes each element of these TMD+INPUT
> pairs.

Which is still just a countable infinite number of inputs, with an
uncountable infinte number of functions to compute.

>
>> Since you seem to have problems understanding the countable infinite,
>> I don't expect you to understand the uncountable infinite.
>
>
> Reals are construed as uncountably infinite because there has previously
> been no way to uniquely identify a pair of immediately adjacent points
> on a number line. The assumption has always been that there is always a
> point between two points thus no two points are immediately adjacent.

First note, I didn't say mapping to the Real, I said an uncountable
infinite set, so the same size as the reals, but is a different set.

To show they are countable, you need to show a bijection of EVERY real
to the counting numbers. (or every function over N to the counting Numbers)
>
> Using interval notation we can see that the line segment specified by
> [0,1] is exactly one geometric point longer then the line segment
> specified by [0,1). Thus the point at the right end of [0,1] is
> immediately adjacent to point at the right end of [0,1) with no points
> in-between.
>

Except that there is no such thing.

What IS that point immediately adjacent to the number 1?

This is the problem when dealing with "Dense" number systems.

Note, even with the countable Rational numbers, there is no number
"adjacent" to another, and no "In order" Bijection of rational numbers
to the Natural Numbers.

You clearly do not understand how the infinite (and infinitesimal) work.

Re: The problem of not enough TM for every decision problem has been resolved

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The problem of not enough TM for every decision problem has been
resolved
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 by: olcott - Sat, 7 Jan 2023 18:49 UTC

On 1/7/2023 12:41 PM, Richard Damon wrote:
> On 1/7/23 1:19 PM, olcott wrote:
>> On 1/7/2023 11:23 AM, Richard Damon wrote:
>>> On 1/7/23 12:07 PM, olcott wrote:
>>>> A UTM processes a subset of the set of finite strings such that
>>>> the first string TM description is concatenated to its input
>>>> forming the complete set of every TMD + INPUT combination.
>>>>
>>>> All of the finite strings left over from the set of finite strings
>>>> are totally irrelevant because the complete set of decision problems
>>>> has already been specified.
>>>>
>>>>
>>>
>>> But the subset is just the same size as the set of finite strings
>>> since they both are of size "countable infinity".
>>>
>>
>> Although it may be conventional to say it that way the set of finite
>> strings that are prepended with a valid TMD is a proper subset of the
>> set of all finite strings.
>
> But it is still just
>
>>
>>> This is one of the "confusing" properties of countably infinite sets,
>>> countably infinite proper subsets are still the same size as there
>>> proper super set.
>>>
>>
>> If this means that conventional set theory claims that a proper subset
>> of a set is also an identical set to this set then conventional set
>> theory is wrong.
>>
>
> No, not identical, just the same size.
>

Even though conventional, it is incorrect to say that a proper subset of
a set has the same size as the set.

> This is part of the confusing thing with infinite numbers.
>
>>> The problem is (if I am remembering right) that the number of
>>> decision problems isn't a countably infinte number, but an
>>> uncountable infinite, which IS larger than the number of finite
>>> strings that could be given to a UTM, since that is, BY DEFINITION,
>>> countable.
>>>
>>
>> Yes that is the mistake of conventional wisdom.
>> An infinite set of unique TMD's has each element of the unique set of
>> finite strings appended. A UTM processes each element of these TMD+INPUT
>> pairs.
>
> Which is still just a countable infinite number of inputs, with an
> uncountable infinte number of functions to compute.
>
>>
>>> Since you seem to have problems understanding the countable infinite,
>>> I don't expect you to understand the uncountable infinite.
>>
>>
>> Reals are construed as uncountably infinite because there has previously
>> been no way to uniquely identify a pair of immediately adjacent points
>> on a number line. The assumption has always been that there is always a
>> point between two points thus no two points are immediately adjacent.
>
> First note, I didn't say mapping to the Real, I said an uncountable
> infinite set, so the same size as the reals, but is a different set.

Reals are also construed as an uncountable infinite set.

>
> To show they are countable, you need to show a bijection of EVERY real
> to the counting numbers. (or every function over N to the counting Numbers)
>>
>> Using interval notation we can see that the line segment specified by
>> [0,1] is exactly one geometric point longer then the line segment
>> specified by [0,1). Thus the point at the right end of [0,1] is
>> immediately adjacent to point at the right end of [0,1) with no points
>> in-between.
>>
>
> Except that there is no such thing.
>
> What IS that point immediately adjacent to the number 1?

The right point of the line segment [0,1) is immediately adjacent to 1.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: The problem of not enough TM for every decision problem has been resolved

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<tpcera$3ir4l$1@dont-email.me>
From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sat, 7 Jan 2023 19:49 UTC

On 1/7/23 1:49 PM, olcott wrote:
> On 1/7/2023 12:41 PM, Richard Damon wrote:
>> On 1/7/23 1:19 PM, olcott wrote:
>>> On 1/7/2023 11:23 AM, Richard Damon wrote:
>>>> On 1/7/23 12:07 PM, olcott wrote:
>>>>> A UTM processes a subset of the set of finite strings such that
>>>>> the first string TM description is concatenated to its input
>>>>> forming the complete set of every TMD + INPUT combination.
>>>>>
>>>>> All of the finite strings left over from the set of finite strings
>>>>> are totally irrelevant because the complete set of decision problems
>>>>> has already been specified.
>>>>>
>>>>>
>>>>
>>>> But the subset is just the same size as the set of finite strings
>>>> since they both are of size "countable infinity".
>>>>
>>>
>>> Although it may be conventional to say it that way the set of finite
>>> strings that are prepended with a valid TMD is a proper subset of the
>>> set of all finite strings.
>>
>> But it is still just
>>
>>>
>>>> This is one of the "confusing" properties of countably infinite
>>>> sets, countably infinite proper subsets are still the same size as
>>>> there proper super set.
>>>>
>>>
>>> If this means that conventional set theory claims that a proper subset
>>> of a set is also an identical set to this set then conventional set
>>> theory is wrong.
>>>
>>
>> No, not identical, just the same size.
>>
>
> Even though conventional, it is incorrect to say that a proper subset of
> a set has the same size as the set.
>

Why? You comment just shows an failure to understand how infinite
numbers work.

In fact, if you TRY to make that sort of logic work, you get
inconsistencies.

This comes form things like the set of all even numers is BOTH a subset
of all the Natural Numbers (removing all the odd numbers) or just a
relabeling of the set of Natural Numbers (replacing each one with twice
itself).

These are EXACTLY the same set, so the set of all even numbers must be
bigger than itself with your logic.

>> This is part of the confusing thing with infinite numbers.
>>
>>>> The problem is (if I am remembering right) that the number of
>>>> decision problems isn't a countably infinte number, but an
>>>> uncountable infinite, which IS larger than the number of finite
>>>> strings that could be given to a UTM, since that is, BY DEFINITION,
>>>> countable.
>>>>
>>>
>>> Yes that is the mistake of conventional wisdom.
>>> An infinite set of unique TMD's has each element of the unique set of
>>> finite strings appended. A UTM processes each element of these TMD+INPUT
>>> pairs.
>>
>> Which is still just a countable infinite number of inputs, with an
>> uncountable infinte number of functions to compute.
>>
>>>
>>>> Since you seem to have problems understanding the countable
>>>> infinite, I don't expect you to understand the uncountable infinite.
>>>
>>>
>>> Reals are construed as uncountably infinite because there has previously
>>> been no way to uniquely identify a pair of immediately adjacent points
>>> on a number line. The assumption has always been that there is always a
>>> point between two points thus no two points are immediately adjacent.
>>
>> First note, I didn't say mapping to the Real, I said an uncountable
>> infinite set, so the same size as the reals, but is a different set.
>
> Reals are also construed as an uncountable infinite set.

Yep, but a DIFFERENT uncountable infiite set.

>
>>
>> To show they are countable, you need to show a bijection of EVERY real
>> to the counting numbers. (or every function over N to the counting
>> Numbers)
>>>
>>> Using interval notation we can see that the line segment specified by
>>> [0,1] is exactly one geometric point longer then the line segment
>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>> immediately adjacent to point at the right end of [0,1) with no points
>>> in-between.
>>>
>>
>> Except that there is no such thing.
>>
>> What IS that point immediately adjacent to the number 1?
>
> The right point of the line segment [0,1) is immediately adjacent to 1.
>
>

Which is?

You can't name it, because it isn't a unique pooint with a value.

So it just doesn't exist.

This shows your ignorance on the topic.

You REPEATEDLY make this sort of mistake when dealing with infinite
sets, it appears, because you puny brain just can't comprehend them.

Re: The problem of not enough TM for every decision problem has been resolved

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The problem of not enough TM for every decision problem has been
resolved
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 by: olcott - Sat, 7 Jan 2023 20:25 UTC

On 1/7/2023 1:49 PM, Richard Damon wrote:
> On 1/7/23 1:49 PM, olcott wrote:
>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>> On 1/7/23 1:19 PM, olcott wrote:
>>>> On 1/7/2023 11:23 AM, Richard Damon wrote:
>>>>> On 1/7/23 12:07 PM, olcott wrote:
>>>>>> A UTM processes a subset of the set of finite strings such that
>>>>>> the first string TM description is concatenated to its input
>>>>>> forming the complete set of every TMD + INPUT combination.
>>>>>>
>>>>>> All of the finite strings left over from the set of finite strings
>>>>>> are totally irrelevant because the complete set of decision problems
>>>>>> has already been specified.
>>>>>>
>>>>>>
>>>>>
>>>>> But the subset is just the same size as the set of finite strings
>>>>> since they both are of size "countable infinity".
>>>>>
>>>>
>>>> Although it may be conventional to say it that way the set of finite
>>>> strings that are prepended with a valid TMD is a proper subset of the
>>>> set of all finite strings.
>>>
>>> But it is still just
>>>
>>>>
>>>>> This is one of the "confusing" properties of countably infinite
>>>>> sets, countably infinite proper subsets are still the same size as
>>>>> there proper super set.
>>>>>
>>>>
>>>> If this means that conventional set theory claims that a proper subset
>>>> of a set is also an identical set to this set then conventional set
>>>> theory is wrong.
>>>>
>>>
>>> No, not identical, just the same size.
>>>
>>
>> Even though conventional, it is incorrect to say that a proper subset
>> of a set has the same size as the set.
>>
>
> Why? You comment just shows an failure to understand how infinite
> numbers work.
>
> In fact, if you TRY to make that sort of logic work, you get
> inconsistencies.
>
> This comes form things like the set of all even numers is BOTH a subset
> of all the Natural Numbers (removing all the odd numbers) or just a
> relabeling of the set of Natural Numbers (replacing each one with twice
> itself).
>
> These are EXACTLY the same set, so the set of all even numbers must be
> bigger than itself with your logic.
>
>>> This is part of the confusing thing with infinite numbers.
>>>
>>>>> The problem is (if I am remembering right) that the number of
>>>>> decision problems isn't a countably infinte number, but an
>>>>> uncountable infinite, which IS larger than the number of finite
>>>>> strings that could be given to a UTM, since that is, BY DEFINITION,
>>>>> countable.
>>>>>
>>>>
>>>> Yes that is the mistake of conventional wisdom.
>>>> An infinite set of unique TMD's has each element of the unique set of
>>>> finite strings appended. A UTM processes each element of these
>>>> TMD+INPUT
>>>> pairs.
>>>
>>> Which is still just a countable infinite number of inputs, with an
>>> uncountable infinte number of functions to compute.
>>>
>>>>
>>>>> Since you seem to have problems understanding the countable
>>>>> infinite, I don't expect you to understand the uncountable infinite.
>>>>
>>>>
>>>> Reals are construed as uncountably infinite because there has
>>>> previously
>>>> been no way to uniquely identify a pair of immediately adjacent points
>>>> on a number line. The assumption has always been that there is always a
>>>> point between two points thus no two points are immediately adjacent.
>>>
>>> First note, I didn't say mapping to the Real, I said an uncountable
>>> infinite set, so the same size as the reals, but is a different set.
>>
>> Reals are also construed as an uncountable infinite set.
>
> Yep, but a DIFFERENT uncountable infiite set.
>
>>
>>>
>>> To show they are countable, you need to show a bijection of EVERY
>>> real to the counting numbers. (or every function over N to the
>>> counting Numbers)
>>>>
>>>> Using interval notation we can see that the line segment specified
>>>> by [0,1] is exactly one geometric point longer then the line segment
>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>> immediately adjacent to point at the right end of [0,1) with no points
>>>> in-between.
>>>>
>>>
>>> Except that there is no such thing.
>>>
>>> What IS that point immediately adjacent to the number 1?
>>
>> The right point of the line segment [0,1) is immediately adjacent to 1.
>>
>>
>
> Which is?
>
> You can't name it, because it isn't a unique pooint with a value.
>
> So it just doesn't exist.
It is a point that is uniquely identified as the rightmost point of the
following line segment [0,1).

The conventional meaning of interval notation knows that there are no
points between the rightmost point of the line segment [0,1] and the
rightmost point of the line segment [0,1).

There is a bijection between each of these points and a real number,
thus specifying a pair of real numbers that are immediately adjacent to
each other.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: The problem of not enough TM for every decision problem has been resolved

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sat, 7 Jan 2023 20:38 UTC

On 1/7/23 3:25 PM, olcott wrote:
> On 1/7/2023 1:49 PM, Richard Damon wrote:
>> On 1/7/23 1:49 PM, olcott wrote:
>>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>>> On 1/7/23 1:19 PM, olcott wrote:
>>>>> Using interval notation we can see that the line segment specified
>>>>> by [0,1] is exactly one geometric point longer then the line segment
>>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>>> immediately adjacent to point at the right end of [0,1) with no points
>>>>> in-between.
>>>>>
>>>>
>>>> Except that there is no such thing.
>>>>
>>>> What IS that point immediately adjacent to the number 1?
>>>
>>> The right point of the line segment [0,1) is immediately adjacent to 1.
>>>
>>>
>>
>> Which is?
>>
>> You can't name it, because it isn't a unique pooint with a value.
>>
>> So it just doesn't exist.
> It is a point that is uniquely identified as the rightmost point of the
> following line segment [0,1).

Except what ever point x you name, has another point closer with a value
of (x+1)/2

>
> The conventional meaning of interval notation knows that there are no
> points between the rightmost point of the line segment [0,1] and the
> rightmost point of the line segment [0,1).

No it means all the points 0 <= x < 1, or the points on the line
excluding that end point.

The definition NEVER talks of the "right most point" that is just less
than 1.

>
> There is a bijection between each of these points and a real number,
> thus specifying a pair of real numbers that are immediately adjacent to
> each other.
>

Nope, you don't biject to "a real number", you biject the elements of a set.

Bijectection also doesn't define "adjacent".

You are just showing you don't know what you are talking about.

Your brain just don't understand the concepts, so of course you are
confused.

Re: The problem of not enough TM for every decision problem has been resolved

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The problem of not enough TM for every decision problem has been
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 by: olcott - Sat, 7 Jan 2023 20:53 UTC

On 1/7/2023 2:38 PM, Richard Damon wrote:
> On 1/7/23 3:25 PM, olcott wrote:
>> On 1/7/2023 1:49 PM, Richard Damon wrote:
>>> On 1/7/23 1:49 PM, olcott wrote:
>>>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>>>> On 1/7/23 1:19 PM, olcott wrote:
>>>>>> Using interval notation we can see that the line segment specified
>>>>>> by [0,1] is exactly one geometric point longer then the line segment
>>>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>>>> immediately adjacent to point at the right end of [0,1) with no
>>>>>> points
>>>>>> in-between.
>>>>>>
>>>>>
>>>>> Except that there is no such thing.
>>>>>
>>>>> What IS that point immediately adjacent to the number 1?
>>>>
>>>> The right point of the line segment [0,1) is immediately adjacent to 1.
>>>>
>>>>
>>>
>>> Which is?
>>>
>>> You can't name it, because it isn't a unique pooint with a value.
>>>
>>> So it just doesn't exist.
>> It is a point that is uniquely identified as the rightmost point of the
>> following line segment [0,1).
>
> Except what ever point x you name, has another point closer with a value
> of (x+1)/2
>
>>
>> The conventional meaning of interval notation knows that there are no
>> points between the rightmost point of the line segment [0,1] and the
>> rightmost point of the line segment [0,1).
>
> No it means all the points 0 <= x < 1, or the points on the line
> excluding that end point.
>
> The definition NEVER talks of the "right most point" that is just less
> than 1.
>

None the less it does specify a rightmost point that is immediately
adjacent to 1

>>
>> There is a bijection between each of these points and a real number,
>> thus specifying a pair of real numbers that are immediately adjacent to
>> each other.
>>
>
> Nope, you don't biject to "a real number", you biject the elements of a
> set.
>
> Bijectection also doesn't define "adjacent".
>

Every point on a number line has a unique corresponding real number.
I did uniquely identify a pair of points on a number line that are
immediately adjacent. Therefore these points must correspond to Real
numbers that are immediately adjacent.

> You are just showing you don't know what you are talking about.
>
> Your brain just don't understand the concepts, so of course you are
> confused.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: The problem of not enough TM for every decision problem has been resolved

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 by: Richard Damon - Sat, 7 Jan 2023 21:19 UTC

On 1/7/23 3:53 PM, olcott wrote:
> On 1/7/2023 2:38 PM, Richard Damon wrote:
>> On 1/7/23 3:25 PM, olcott wrote:
>>> On 1/7/2023 1:49 PM, Richard Damon wrote:
>>>> On 1/7/23 1:49 PM, olcott wrote:
>>>>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>>>>> On 1/7/23 1:19 PM, olcott wrote:
>>>>>>> Using interval notation we can see that the line segment
>>>>>>> specified by [0,1] is exactly one geometric point longer then the
>>>>>>> line segment
>>>>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>>>>> immediately adjacent to point at the right end of [0,1) with no
>>>>>>> points
>>>>>>> in-between.
>>>>>>>
>>>>>>
>>>>>> Except that there is no such thing.
>>>>>>
>>>>>> What IS that point immediately adjacent to the number 1?
>>>>>
>>>>> The right point of the line segment [0,1) is immediately adjacent
>>>>> to 1.
>>>>>
>>>>>
>>>>
>>>> Which is?
>>>>
>>>> You can't name it, because it isn't a unique pooint with a value.
>>>>
>>>> So it just doesn't exist.
>>> It is a point that is uniquely identified as the rightmost point of the
>>> following line segment [0,1).
>>
>> Except what ever point x you name, has another point closer with a
>> value of (x+1)/2
>>
>>>
>>> The conventional meaning of interval notation knows that there are no
>>> points between the rightmost point of the line segment [0,1] and the
>>> rightmost point of the line segment [0,1).
>>
>> No it means all the points 0 <= x < 1, or the points on the line
>> excluding that end point.
>>
>> The definition NEVER talks of the "right most point" that is just less
>> than 1.
>>
>
> None the less it does specify a rightmost point that is immediately
> adjacent to 1

Nope, because what ever point you try to chose, there is one closer.

This is called the Density property.

The term "Right Most Point" in an (half) open interval is an
Epistemological Antinomy.

>
>>>
>>> There is a bijection between each of these points and a real number,
>>> thus specifying a pair of real numbers that are immediately adjacent to
>>> each other.
>>>
>>
>> Nope, you don't biject to "a real number", you biject the elements of
>> a set.
>>
>> Bijectection also doesn't define "adjacent".
>>
>
> Every point on a number line has a unique corresponding real number.
> I did uniquely identify a pair of points on a number line that are
> immediately adjacent. Therefore these points must correspond to Real
> numbers that are immediately adjacent.

Right, but the problem is the assumption that there IS an "adjacent"
point on the line.

Every point you chose correspondes to a Real Number, and between any two
real numbers, as between any to points on a line, is another real
number/point on the line.

They are "Dense"

As, it seems, are you.

You are just proving your ignorance of these things.

>
>
>> You are just showing you don't know what you are talking about.
>>
>> Your brain just don't understand the concepts, so of course you are
>> confused.
>

Re: The problem of not enough TM for every decision problem has been resolved

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From: polco...@gmail.com (olcott)
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Subject: Re: The problem of not enough TM for every decision problem has been
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 by: olcott - Sat, 7 Jan 2023 21:31 UTC

On 1/7/2023 3:19 PM, Richard Damon wrote:
> On 1/7/23 3:53 PM, olcott wrote:
>> On 1/7/2023 2:38 PM, Richard Damon wrote:
>>> On 1/7/23 3:25 PM, olcott wrote:
>>>> On 1/7/2023 1:49 PM, Richard Damon wrote:
>>>>> On 1/7/23 1:49 PM, olcott wrote:
>>>>>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>>>>>> On 1/7/23 1:19 PM, olcott wrote:
>>>>>>>> Using interval notation we can see that the line segment
>>>>>>>> specified by [0,1] is exactly one geometric point longer then
>>>>>>>> the line segment
>>>>>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>>>>>> immediately adjacent to point at the right end of [0,1) with no
>>>>>>>> points
>>>>>>>> in-between.
>>>>>>>>
>>>>>>>
>>>>>>> Except that there is no such thing.
>>>>>>>
>>>>>>> What IS that point immediately adjacent to the number 1?
>>>>>>
>>>>>> The right point of the line segment [0,1) is immediately adjacent
>>>>>> to 1.
>>>>>>
>>>>>>
>>>>>
>>>>> Which is?
>>>>>
>>>>> You can't name it, because it isn't a unique pooint with a value.
>>>>>
>>>>> So it just doesn't exist.
>>>> It is a point that is uniquely identified as the rightmost point of the
>>>> following line segment [0,1).
>>>
>>> Except what ever point x you name, has another point closer with a
>>> value of (x+1)/2
>>>
>>>>
>>>> The conventional meaning of interval notation knows that there are no
>>>> points between the rightmost point of the line segment [0,1] and the
>>>> rightmost point of the line segment [0,1).
>>>
>>> No it means all the points 0 <= x < 1, or the points on the line
>>> excluding that end point.
>>>
>>> The definition NEVER talks of the "right most point" that is just
>>> less than 1.
>>>
>>
>> None the less it does specify a rightmost point that is immediately
>> adjacent to 1
>
> Nope, because what ever point you try to chose, there is one closer.
>
> This is called the Density property.
>
>
You can assume that yet interval notation contradicts you.
I will clarify the right point (not rightmost point) of the line segment
specified by [0,1) is immediately adjacent to 1.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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From: Rich...@Damon-Family.org (Richard Damon)
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Date: Sat, 7 Jan 2023 16:39:16 -0500
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 by: Richard Damon - Sat, 7 Jan 2023 21:39 UTC

On 1/7/23 4:31 PM, olcott wrote:
> On 1/7/2023 3:19 PM, Richard Damon wrote:
>> On 1/7/23 3:53 PM, olcott wrote:
>>> On 1/7/2023 2:38 PM, Richard Damon wrote:
>>>> On 1/7/23 3:25 PM, olcott wrote:
>>>>> On 1/7/2023 1:49 PM, Richard Damon wrote:
>>>>>> On 1/7/23 1:49 PM, olcott wrote:
>>>>>>> On 1/7/2023 12:41 PM, Richard Damon wrote:
>>>>>>>> On 1/7/23 1:19 PM, olcott wrote:
>>>>>>>>> Using interval notation we can see that the line segment
>>>>>>>>> specified by [0,1] is exactly one geometric point longer then
>>>>>>>>> the line segment
>>>>>>>>> specified by [0,1). Thus the point at the right end of [0,1] is
>>>>>>>>> immediately adjacent to point at the right end of [0,1) with no
>>>>>>>>> points
>>>>>>>>> in-between.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except that there is no such thing.
>>>>>>>>
>>>>>>>> What IS that point immediately adjacent to the number 1?
>>>>>>>
>>>>>>> The right point of the line segment [0,1) is immediately adjacent
>>>>>>> to 1.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Which is?
>>>>>>
>>>>>> You can't name it, because it isn't a unique pooint with a value.
>>>>>>
>>>>>> So it just doesn't exist.
>>>>> It is a point that is uniquely identified as the rightmost point of
>>>>> the
>>>>> following line segment [0,1).
>>>>
>>>> Except what ever point x you name, has another point closer with a
>>>> value of (x+1)/2
>>>>
>>>>>
>>>>> The conventional meaning of interval notation knows that there are no
>>>>> points between the rightmost point of the line segment [0,1] and the
>>>>> rightmost point of the line segment [0,1).
>>>>
>>>> No it means all the points 0 <= x < 1, or the points on the line
>>>> excluding that end point.
>>>>
>>>> The definition NEVER talks of the "right most point" that is just
>>>> less than 1.
>>>>
>>>
>>> None the less it does specify a rightmost point that is immediately
>>> adjacent to 1
>>
>> Nope, because what ever point you try to chose, there is one closer.
>>
>> This is called the Density property.
>>
>>
> You can assume that yet interval notation contradicts you.
> I will clarify the right point (not rightmost point) of the line segment
> specified by [0,1) is immediately adjacent to 1.
>

Nope, no point exist that IS the "Right" point.

(And what does that "Right" mean other than "Rightmost", you have a
semantics problem there)

There is no "Right EndPoint" of that line segment, that is why it is
called an "Open Interval" and drawn with an open circle on the end,
because it is a line missing its rightmost point, and no other point
becomes the rightmost because no unique point exists that is it.

Again, what ever point you try to name, there will be another one to its
right that is still on the open line segment.

And, none of this is getting you any closer to making the COUNTABLE
infiite set of Turing Machine catch up to the UNCOUNTABLE infinite set
of possible functions to try to compute.

And, you are just digging the grave of your reputation deeper with your
demonstration of ignorance of the actual working of the things you claim
to know about.

It is clear you don't understand the first principle of knowledge, you
aren't supposed to let yourself "know" something that isn't actually true.

You run into this problem because you have adopted broken logic.

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