2 ms·
All the numbers we can use are computable (how can you use a number if you can't actually talk about it?) and there are only countably many of those.
by bobbylarrybobby 4y ago
All the numbers we can use are computable (how can you use a number if you can't actually talk about it?) and there are only countably many of those.
- ChrisLomont 4y ago>All the numbers we can use are computable That's not true :) A nice example is Chaitin's constant [1], which I can use in proof and books and define and on and on.... And it's explicitly and most definitely NOT computable :) There are lots of numbers in lots of areas of mathematics, even symbolic mathematics that are not computable in the sense you want them to be computable. Chaitin's constant is the tip of a very big iceberg. You're using circular logic by claiming the only numbers I can are are the computable ones then claiming all numbers I can use are computable. That's not true. It's a circular argument. [1] https://en.wikipedia.org/wiki/Chaitin%27s_constant https://en.wikipedia.org/wiki/Chaitin%27s_constant