Prev: Question for Aatu Koskensilta
Next: Godels incompleteness theorem are invalid ie illegitimate
From: |-|ercules on 15 Jun 2010 23:34
"Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote
> Cantor said and proved that
> any purported list of all Reals cannot contain all Reals. His proof is
> simple and clear, provides an explicit construction of at least one
> missing Real.


Like so...

123
456
789

Diag = 159
Anti-diag = 260

Where are you getting a (missing real) '260' when

>the list of computable reals contain every digit of ALL possible infinite
>sequences (3)


___________________________________________________________________

"Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote
>>the list of computable reals contain every digit of ALL possible infinite
>>sequences (3)
>>
>>OK does everyone get (1) (2) and (3).
>
> If you state it carefully, then yes, everyone gets it:

___________________________________________________________________



Herc

From: Math-a-nator on 16 Jun 2010 01:35
http://upload.wikimedia.org/wikipedia/commons/thumb/8/89/Trenecito.jpg/364px-Trenecito.jpg


From: George Greene on 16 Jun 2010 01:35
On Jun 15, 11:34 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> Where are you getting a (missing real) '260' when
>
> >the list of computable reals contain every digit of ALL possible infinite
> >sequences

IT DOESN'T, DUMBASS.
The only reason you THINK it does is because YOU CAN'T SPEAK ENGLISH.
There are ONLY TEN digits in this numeration system!
"All you have to do to contain every digit" is contain all 10 of them,
which
you can do EITHER in the 1x10 list
0123456789,
OR in the 10x1 list below!

You do NOT NEED to use a list of infinitely wide "computable" reals
(let alone the list of ALL of them, which is a list that itself IS NOT
computable)
in order to "contain every digit of ALL possible infinite sequences".

The infinite list of all possible FINITE sequences (which IS
computable)
ALSO "contains", in YOUR sense of "contain" (a word which you
personally
are WAY TOO STUPID TO EVEN DEFINE) "every digit of all possible
infinite sequences".

In English, the phrase "every digit" IS SINGULAR. It generalizes over
multiple
cases, each of which means ONE digit. It means each and every digit
TAKEN INDIVIDUALLY.
For that reason, IN ADDITION to accomplishing your goal of
"containing every digit of ALL possible infinite sequences"
by using only the list of finite sequences, YOU COULD ALSO
accomplish that goal using the following VERY finite 10x1 list:
0
1
2
3
4
5
6
7
8
9
..
THAT list contains every digit of all possible infinite sequences,
since every digit IS ONE OF those 10 (in that number-base).

If you are going to require one element of the list to contain
multiple digits
from the sequence in the correct order, then, OBVIOUSLY, NO computable
real contains "every digit of" ANY (infinite) non-computable sequence
("infinite" was in parentheses because every non-computable sequence
has to be infinite). If it contained ALL digits of some non-
computable
sequence (in the correct order and occurring the correct number of
times,
which, for at least two of the 10 digits, will be infinitely often),
then IT WOULD BE
EQUAL to the non-computable sequence, which would contradict the fact
that
it was computable.

digit (in order) then it would be EQUAL to
From: George Greene on 16 Jun 2010 01:36
Your subject line IS STUPID,Herc.
Contradictions CANNOT be SPOTTED!
They HAVE to be PROVED, INSTEAD!
There is NO SUCH THING as a contradiction that
your readers "can't spot"! If YOU HAVEN'T PROVED that
there is a contradiction, then it is YOU who haven't spotted it!

From: |-|ercules on 16 Jun 2010 05:39
"George Greene" <greeneg(a)email.unc.edu> wrote
> On Jun 15, 11:34 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
>> Where are you getting a (missing real) '260' when
>>
>> >the list of computable reals contain every digit of ALL possible infinite
>> >sequences
>
> IT DOESN'T, DUMBASS.
> The only reason you THINK it does is because YOU CAN'T SPEAK ENGLISH.
> There are ONLY TEN digits in this numeration system!
> "All you have to do to contain every digit" is contain all 10 of them,
> which
> you can do EITHER in the 1x10 list
> 0123456789,
> OR in the 10x1 list below!
>
> You do NOT NEED to use a list of infinitely wide "computable" reals
> (let alone the list of ALL of them, which is a list that itself IS NOT
> computable)
> in order to "contain every digit of ALL possible infinite sequences".
>
> The infinite list of all possible FINITE sequences (which IS
> computable)
> ALSO "contains", in YOUR sense of "contain" (a word which you
> personally
> are WAY TOO STUPID TO EVEN DEFINE) "every digit of all possible
> infinite sequences".
>
> In English, the phrase "every digit" IS SINGULAR. It generalizes over
> multiple
> cases, each of which means ONE digit. It means each and every digit
> TAKEN INDIVIDUALLY.
> For that reason, IN ADDITION to accomplishing your goal of
> "containing every digit of ALL possible infinite sequences"
> by using only the list of finite sequences, YOU COULD ALSO
> accomplish that goal using the following VERY finite 10x1 list:
> 0
> 1
> 2
> 3
> 4
> 5
> 6
> 7
> 8
> 9
> .
> THAT list contains every digit of all possible infinite sequences,
> since every digit IS ONE OF those 10 (in that number-base).
>
> If you are going to require one element of the list to contain
> multiple digits
> from the sequence in the correct order, then, OBVIOUSLY, NO computable
> real contains "every digit of" ANY (infinite) non-computable sequence
> ("infinite" was in parentheses because every non-computable sequence
> has to be infinite). If it contained ALL digits of some non-
> computable
> sequence (in the correct order and occurring the correct number of
> times,
> which, for at least two of the 10 digits, will be infinitely often),
> then IT WOULD BE
> EQUAL to the non-computable sequence, which would contradict the fact
> that
> it was computable.
>
> digit (in order) then it would be EQUAL to

............?


Why didn't you speak up in YESTERDAY'S topic?

***>the list of computable reals contain every digit of ALL possible infinite sequences (3)

***>OK does everyone get (1) (2) and (3).


defn(herc_cant_3)
The list of computable reals contains every digit (in order) of all possible infinite sequences.

Derivation

Given the increasing finite prefixes of pi

3
31
314
...

This list contains every digit (in order) of the infinite expansion of pi.

Given the increasing finite prefixes of e

2
27
271
...

This list contains every digit (in order) of the infinite expansion of e.

Given the increasing finite prefixes of ALL infinite expansions,
that list contains every digit (in order) of every infinite expansion.

So herc_cant_3 is true.
The list of computable reals contains every digit (in order) of all possible infinite sequences.

Herc

 |  Next  |  Last
Pages: 1 2 3
Prev: Question for Aatu Koskensilta
Next: Godels incompleteness theorem are invalid ie illegitimate