I Can Cantor's diagonal number solve the issue of infinite lists?

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Cantor's diagonal argument demonstrates that the set of real numbers in the interval [0,1] is uncountable, regardless of whether the representation is in binary or decimal. The discussion highlights that while different bases may complicate the proof, they do not invalidate it; a proof in one base suffices. It emphasizes that the uniqueness of decimal expansions and the handling of infinite sequences are crucial to the argument's validity. The participants also note that any valid proof must account for the representation of numbers without ambiguity, such as avoiding infinite sequences of 9's. Ultimately, the essence of Cantor's argument remains intact across different numerical systems.
  • #61
One can use the decimal representation of the real numbers that everyone is familiar with since 4th grade and avoid the 999... issue simply by never allowing the infinite 9 representation in the list and never using 9 on the diagonal. That is concrete and familiar and does not require any abstraction to infinite lists. IMO, abstraction to the general list is easier to motivate after seeing a concrete example.
 
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  • #62
JeffJo said:
Do you disagree with any of this?
Nope. You win.
 
  • #63
FactChecker said:
One can use the decimal representation of the real numbers that everyone is familiar with since 4th grade and avoid the 999... issue simply by never allowing the infinite 9 representation in the list and never using 9 on the diagonal. That is concrete and familiar and does not require any abstraction to infinite lists. IMO, abstraction to the general list is easier to motivate after seeing a concrete example.
Sounds eminently reasonable to me.
 
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