Talk:Cantor's diagonal argument

message: Moved to arguments page. --Trovatore (talk) 06:30, 16 July 2021 (UTC)
thread_title:  Set of all sets 

message: Moved to arguments page. --Trovatore (talk) 06:30, 16 July 2021 (UTC)
thread_title:  diagonal counterexample 

message: "In his 1891 article, Cantor considered the set T of all infinite sequences of binary digits (i.e. each digit is zero or one):"
No, he didn't. In his 1891 article, Cantor considered a bicoloring by m and w. It is standard in wikipedia for modified proofs to be indicated as such and it is amateurish not to do so when the article itself is referred to by date and linked to in the footnotes. The proof should either conform to the reference or (if we're so endeared to the modification that we prefer it to the original) be indicated as an updated or simplified restatement thereof.  — Preceding unsigned comment added by 2603:7000:8E03:3E7E:6979:D94F:B78E:B1DA (talk) 18:56, 15 November 2021 (UTC)
thread_title:  In his 1891 article... 

message: like so many math/logic/science articles, this is not written for the average user 
why are you math people so bad at describing stuff in terms an ordinary person can understand ? 
that is mean; that is just reality
— Preceding unsigned comment added by 2601:197:d00:3ca0:adb1:4bc0:d097:b9a6 (talk) 04:12, 21 February 2024 (UTC)
replies: text: You are more than welcome to suggest improvements to the article, including ways it can be made more understandable to more readers. --Trovatore (talk) 20:30, 23 February 2024 (UTC)
replies: text: Nice paradox! He says he can't understand it so you suggest he rephrases it!  :) BioImages2000 (talk) 11:49, 21 May 2024 (UTC)
replies: text:  There was no actionable complaint in the post.  Comments that just whine about the article being too hard to understand are of minimal value.  If they give specifics as to where they're getting stuck, there might be something to fix.  --Trovatore (talk) 21:10, 21 May 2024 (UTC)
thread_title:  not written for the average user 

message: The page needs to clearly state that these strings of digits represent binary fractions between 0 and 1 inclusive.
This version of the proof differs from Cantor's original in two ways:
(1) it uses base 2 numbers instead of base 10 numbers; and
(2) it uses arbitrary strings of digits--which include leading zeros--
rather than place notation.
The proof as given holds for arbitrary strings of digits, but not 
if the digits are interpreted as numbers.
When digits are used to express whole numbers, leading zeros are not significant. 1 = 01 = 001 = 0001 = 000001 etc.  So too with rational and real numbers greater than 1: 1.1 = 01.1 = 001.1  = 0001.1, etc.
That is why Cantor used decimal fractions in [0,1]: 0.1 is different from 0.01. etc.
So in Wiki's form of the proof, to prove that the number 7 is
missing from say a 6 row x 6 column table, one must show that
1 1 1 0 0 0, 0 1 1 1 0 0 , 0 0 1 1 1 0, and 0 0 0 1 1 1 are
missing--since all these numerals represent the same number. 
That is not shown--and indeed is not true--making the proof
(which is otherwise air-tight) invalid. Mgryan (talk) 01:50, 16 May 2024 (UTC)
replies: text: The proof (text between "" and "") uses infinite sequences of binary digits. These are mathematical objects by their own, and are not interpreted as natural or real numbers. Lateron, in subsection Cantor's_diagonal_argument#Real_numbers, the uncountability of the set of real numbers between 0 and 1 is shown as a corollary. - Jochen Burghardt (talk) 05:20, 16 May 2024 (UTC)
thread_title:  Cantor proved this for reals in [0,1]--for a reason