> There's plenty of Turing machines that print out lots of 1s (either finite or infinite), where we can accurately predict in finite time how many it will print out.
The reasoning is not-computable implies an infinity. As you know "implies" is not reflexive, so no I wasn't intending to say the reverse.
> > [...] infinite means non-computable.
You didn't quote the full sentence. It was "because there are infinite numbers to check and infinite means non-computable". Being forced to check an infinite number of possibilities is one definition of non-computable, as you acknowledged.
> The reasoning is not-computable implies an infinity. As you know "implies" is not reflexive, so no I wasn't intending to say the reverse.
OK, but you implied you were giving a definition? Definitions are usually two sided, where every 'if' is silently implied to be an 'iff' for convenience.
> You didn't quote the full sentence. It was "because there are infinite numbers to check and infinite means non-computable". Being forced to check an infinite number of possibilities is one definition of non-computable, as you acknowledged.
Not really. You'd need to prove that you actually need to check the numbers. We need to exclude that we just lacked the right idea.
Eg it fairly easy to prove that there's an infinite amount of prime numbers without having to check all numbers. It was a lot harder to prove Fermat's Last Theorem without checking all the numbers. For the Collatz conjucture, we don't know.
Why I did acknowledge was that _if_ you can prove an upper bound, then checking all numbers is computable, yes.
But if we haven't found an upper bound (yet), we have no clue whether the problem is computable or not.
The reasoning is not-computable implies an infinity. As you know "implies" is not reflexive, so no I wasn't intending to say the reverse.
> > [...] infinite means non-computable.
You didn't quote the full sentence. It was "because there are infinite numbers to check and infinite means non-computable". Being forced to check an infinite number of possibilities is one definition of non-computable, as you acknowledged.