Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

Am 03.12.2024 um 07:01 schrieb Chris M. Thomasson:

Sometimes I like to think of the set of all natural numbers as an n-ary tree, binary here, wrt zero as a main root, so to speak:
              0
            / \
           /   \
          /     \
         /       \
        1         2
       / \       / \
      /   \     /   \
     3     4   5     6
  .........................
 On and on. A lot of math can be applied to it.

Yeah, Trees are important and interesting structures. :-P
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Hint: In the context of set theory we usualy consider IN = {0, 1, 2, 3, ...}. (Simplifies a lot.)
Then the natural numbers just "specify" the "sizes" of finite sets.
card({}) = 0
card({0}) = card({1}) = card({2}) = ... = 1
card({0, 1}) = card({0, 2}) = card({1, 2}) = ... = 2
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