On Monday 25 July 2016 13:46, Rustom Mody wrote: > The bald fact that tests are finite and the actual search space for cases for > anything remotely non-trivial is infinite is undeniable.
I deny it :-P "Infinity" is pretty big. It's *really* big. It's bigger than most people think. You might think your credit card bill last month was big, but infinity is much bigger. Mathematicians deal with numbers which are so unfathomably huge that we can't even talk about them using the ordinary notation we use for ordinary numbers. Take something as unbelievably big as Graham's Number, so big they had to invent specialised notation just to discuss it: http://mathworld.wolfram.com/GrahamsNumber.html http://www.youtube.com/watch?v=XTeJ64KD5cg Let's make it bigger! Square it. No, cube it! Take the factorial! Cube it again! Raise that number to the power of itself! Add one! Compared to infinity, this new number is infinitesimally tiny. Compared to infinity, this new number is barely even there. Compared to infinity, that new number might as well be zero. Given that any actual program has to *exist* in order to be tested, it must be finite in size. Since the observable universe contains "merely" something of the order of 10**89 or so elementary particles (electrons, protons, etc) even with the combinatory explosion of possibilities, the upper bound on the number of test cases will be something like (10**89)**(10**89), which is minuscule compared to Graham's Number, let alone our even Vaster number. Which is so far short of infinity that in one sense we can say that it has barely even taken a single step in the direction of infinity. (Of course I realise you were using "infinite" just as hyperbole. I just couldn't resist bringing Graham's Number into the discussion.) -- Steve -- https://mail.python.org/mailman/listinfo/python-list
