alt Hacker NewsYou proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective function exists from definitions to real numbers.
Really, the blurb about "seems impossible to verify this by giving positive instances" contains the tension between constructive math and non-constructive math. Does an unnameable (and undefinable) thing actually exist? If a tree falls in a forest, but no one can hear it, does it make a sound?
> No surjective function exists from definitions to real numbers.
I'm not really up on maths so this is possibly a stupid question, but can't any real number be written as an ASCII string, which is basically an integer number, so there is a direct mapping there?
Or is it because the ASCII number wouldn't be in order that makes the difference?
Or is it that you can't write that mapping as a mathematical function perhaps?