Talk:Cantor's diagonal argument/Arguments: Difference between revisions

Revision as of 20:40, 25 April 2025

Revision as of 23:06, 29 April 2025

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::::Now a question for you; 1. Can the diagonal method create an irrational number or an infinite sequence of rational numbers? 2. If the list does not contain all the numbers, will the diagonal method find a new number that is not on the list? [[User:Krzysztof1137|Krzysztof1137]] ([[User talk:Krzysztof1137|talk]]) 20:59, 21 April 2025 (UTC)

::::Please answer the questions. [[User:Krzysztof1137|Krzysztof1137]] ([[User talk:Krzysztof1137|talk]]) 20:40, 25 April 2025 (UTC)

:::::I am not CiaPan, but:

:::::If you are referring to specifically the method from the article page, then my answers

:::::are both No: ​ That creates/finds a sequence of binary digits, not a real number.

:::::(_That part_ is only to show that the set of

:::::infinite sequences of binary digits is uncountable.)

:::::If you are instead referring to

:::::" ​ the real number such that its part before the decimal point is "0" and for all positions n after the decimal point, the digit in that position is the element of {1,2} with the opposite [[parity]] to the [[parity]] of the digit in position n after the decimal point of the [[Non-uniqueness of decimal representation and notational conventions|standard decimal representation]] of the n-th entry in the list ​ "

:::::, ​ then my answers are both yes: ​ ​ ​ If you get different answers for this case, then:

:::::3. ​ ​ ​ Do you think there is no real number

:::::"such that its part ... entry in the list"

:::::, ​ like how there is no such integer for

:::::"the integer that is greater than all other integers" ​ ?

:::::4. ​ ​ ​ If you indeed think there is no real number

:::::"such that its part ... entry in the list"

:::::, ​ then what about

:::::" ​ the real number such that its part before the decimal point is "0" and for all positions n after the decimal point, the digit in that position is 3? ​ "

:::::?

:::::[[User:JumpDiscont|JumpDiscont]] ([[User talk:JumpDiscont|talk]]) 23:06, 29 April 2025 (UTC)