3 ms·
You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resem
by amavect 1mo ago
You 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?
- onraglanroad 1mo ago> 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?
- onraglanroad 1mo agoActually, and perhaps sadly, I asked an LLM and I understand now. But perhaps that's not such a bad thing that I can get answers to my foolish questions!
- amavect 1mo agoguess I won't respond now :( "what is a real number, anyways" is one of my favorite questions, not foolish at all
- quickthrowman 1mo agoIt’s not a foolish question, you got to learn about Cantor’s diagonal argument!
- xelxebar 1mo agoIt's because most real numbers are uncomputable. That means, most of the time, the only way to check that two numbers (i.e. names) are the same is to spend infinite time looking at all their infinite digits. An unknowable name isn't a very good name, IMHO.