As someone who understands computational theory, I strongly suspect you’re seriously confused about how computational complexity theory works. As I don’t have the time or interest to give a course in computational complexity, might I recommend asking the original question on mathoverflow if you are interested.
In this area, I do not think there is such a hard and fast distinction.
So, how would you phrase the existence of hypercomputation as a mathematical statement?
Presumably something involving recursively enumerable functions...
As someone who understands computational theory, I strongly suspect you’re seriously confused about how computational complexity theory works. As I don’t have the time or interest to give a course in computational complexity, might I recommend asking the original question on mathoverflow if you are interested.
Apologies if that came off as rude.