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From: Daryl McCullough on 9 Jun 2010 18:21
|-|ercules says...
>
>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote ...

>>>ALL (INFINITELY MANY) digits of ALL digit sequences are computable!
>>
>> Okay, that's false, but you seem to believe it. Why?
>
>
>What about
>
>ALL digit sequences are computable to ALL finite lengths.

Once again, your statement is a muddled mess. What is true is
the following:

For every real number r, for every natural number n,
there is a computable real r' such that r' agrees with
r in the first n digits.

Do you understand what the above means? By saying
"ALL digit sequences are computable to ALL finite lengths"
do you mean something different, or do you mean the same
thing?

>I just disagree that specifying
>"it's different at digit N to the Nth real and it's different..."
>literally gives any new sequence of digits that are not computable.

Let's go through it more carefully then. Let L be our list of computable
reals, and let L_1, L_2, ... be the reals on the list. Let r be the
antidiagonal of L.

Do you agree that r is not equal to L_1?
Do you agree that r is not equal to L_2?
Do you agree that r is not equal to L_3?

We can prove the following general statement:

For all n, r is not equal to L_n.

From this it follows that:

r is not on the list L.

Since L is presumed to be the list of all computable reals, it
follows that r is not a computable real.

>Examples don't prove it for the entire domain.

That's why Cantor gave a proof. He didn't just give examples.

--
Daryl McCullough
Ithaca, NY

From: |-|ercules on 9 Jun 2010 18:28
"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>>ALL digit sequences are computable to ALL finite lengths.
>
> Once again, your statement is a muddled mess.

What's not to get?

here's a digit sequence:
31415926...
It's the expansion from arctan(1)*4/10.

Is this digit sequence computable to 5 digits?
Is it computable to 6 digits?
Is it computable to any finite number of digits?
Is it computable to ALL finite lengths?

Where are you getting muddled?

Herc

From: Daryl McCullough on 9 Jun 2010 18:50
|-|ercules says...
>
>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>>>ALL digit sequences are computable to ALL finite lengths.
>>
>> Once again, your statement is a muddled mess.
>
>What's not to get?

Why can't you learn how to use quantifiers? Those make
what you are trying to say much more precise. You need
to take an elementary course in mathematics and logic.
Until then, you can't even ask a question without getting
muddled.

--
Daryl McCullough
Ithaca, NY

From: |-|ercules on 9 Jun 2010 19:16
"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
> |-|ercules says...
>>
>>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>>>>ALL digit sequences are computable to ALL finite lengths.
>>>
>>> Once again, your statement is a muddled mess.
>>
>>What's not to get?
>
> Why can't you learn how to use quantifiers? Those make
> what you are trying to say much more precise. You need
> to take an elementary course in mathematics and logic.
> Until then, you can't even ask a question without getting
> muddled.
>

NO dipsh1t. I have a degree in computer science and I am perfectly
fine using quantifiers.

Now let's go through your idiotic denial one question at a time.

here's a digit sequence:
31415926...
It's the expansion from arctan(1)*4/10.

Is this digit sequence computable to 5 digits?


How do you expect to see your error if you refuse to put your formula into words
so you can understand them?

Herc
From: Daryl McCullough on 9 Jun 2010 20:31
|-|ercules says...
>
>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>> |-|ercules says...
>>>
>>>"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>>>>>ALL digit sequences are computable to ALL finite lengths.
>>>>
>>>> Once again, your statement is a muddled mess.
>>>
>>>What's not to get?
>>
>> Why can't you learn how to use quantifiers? Those make
>> what you are trying to say much more precise. You need
>> to take an elementary course in mathematics and logic.
>> Until then, you can't even ask a question without getting
>> muddled.
>>
>
>NO dipsh1t. I have a degree in computer science and I am perfectly
>fine using quantifiers.

No, you are not.

--
Daryl McCullough
Ithaca, NY

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