If you could build a machine that was able to generate every relevant scientific fact from first principles, do you think it would be done at some point, or that it would never stop?
Proving is just a lossless compression of a statement into axioms. A compression algorithm that does not terminate cannot be claimed to perform a compression.
-
-
Ok, then by that reasoning, a proof should always halt. And there should be no halting problem, other than predicting when it stops, rather than IF it stops.
-
I suspect that you still don't see it? In classical math, Pi is a number with a certain numerical value that can be expressed with a function. In constructive (computational math), Pi is just a function. All values are just decorated integers.
- 2 more replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.