A question on Cantor's second diagonalization argument

In summary, Cantor used two diagonalization arguments in his proof. The first showed that the cardinality of the set of natural numbers is equal to the cardinality of the set of rational numbers. The second argument showed that the cardinality of the set of rational numbers is less than the cardinality of the set of real numbers. This was done by constructing a real number between 0 and 1 that cannot be put in a one-to-one correspondence with any natural number. Although there are some technicalities with the decimal expansions, the overall proof still holds.
  • #36
HallsofIvy,

Pay attention to the fact that you did not write a single word of what I wrote, after what I wrote personally to you.

Because you are a professional mathematician, which is the mentor of the Homework help zone, I think that you can do more then just repeating on the words "non-sense".

For example, Hurkyl helped me to address some idea of mine in a formal definition.

It can be found here: https://www.physicsforums.com/showthread.php?s=&threadid=7315

Please instead of "close the doors" as your first step, I'll appreciate your professional help.


Thank you.


Organic
 
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  • #37

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