This discussion centers on the challenges of engaging with anti-Cantor cranks who dispute the validity of Cantor's diagonalization proof, which demonstrates the uncountability of real numbers. Participants share their experiences and strategies for addressing common arguments, emphasizing that many cranks are resistant to logical reasoning. The consensus is that while some individuals may eventually understand Cantor's proof, many are entrenched in their misconceptions and unlikely to change their views. The discussion highlights the futility of trying to convince those who are not open to reasoned dialogue.
PREREQUISITESMathematicians, educators, and anyone interested in understanding or debating the implications of Cantor's work and the nature of mathematical arguments.
micromass said:It can be proven that the only numbers which have multiple decimal representation are numbers which end in 00000... or 9999...
It's a good thing Cantor didn't use base 6 in his proof.If we take the diagonal in Cantor's prove and change all numbers not equal to 5 to 5, and furthermore change all 5's to 6, then we get a number not on the list and the problem will not show up. That is: a number like 0.55555555... has a unique decimal representation.
Furthermore, there are versions of Cantor's proof which do not work with decimal representation at all!
Antiphon said:It's a good thing there are only a handful of such numbers and not an infinite number of them.
micromass said:There are an infinite number of them.
micromass said:There are an infinite number of them.