It has been conjectured that there is no fastest algorithm for multiplication, among other things. Can somebody give me an example of something that provably has no fastest algorithm for?
?Oh right I think I see. But since there only a finite number of ways of arranging code, then the fastest algorithm has to exist anyway. Unless you're talking about infinite length of code as well?
Of course. The different types of Toom-Cook multiplication are an easy example. Of course there are algorithms that outperform all of them, so they don't satisfy your original question.The question is, is it possible that infinite descending chains also exist?