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No surjective function exists from names to real numbers (diagonalization). With any naming scheme, some unnamed real numbers always remain. On the other hand,
by amavect 1mo ago
No surjective function exists from names to real numbers (diagonalization). With any naming scheme, some unnamed real numbers always remain.
On the other hand, given any real number, I can name it. I'll run out of unique names, since no injective function exists from real numbers to names.
So, some unnamed real numbers will always remain (non-constructively), I can make real numbers that escape a naming scheme (constructively), and no unnameable real numbers exist.
- ithkuil 1mo agoWhat does "naming" mean? Assigning a symbol? But who said that the set of symbols must be countable?
- amavect 1mo agoMy hidden assumption: I said the set of names must be countable! I assumed you would know that naming means assigning a finite string (in the Ithkuil writing system of course). and don't nitpick further or else I'll have to write a proof in Agda or Rocq lol