grumpy-buffalo

I wish the term "true AI" were replaced with "strong AI" or "artificial general intelligence" or some such term. We already have true AI - it's a vast, thriving industry. AlphaGo is obviously a true, legitimate, actual, real, nonfictional example of artificial intelligence, as are Google Search, the Facebook Newsfeed, Siri, the Amazon Echo, etc.

How about just for playing a good game of Go?

If you're interested in computational complexity theory, I recommend "Computational Complexity" by Christos Papadimitriou. It's a classic, though it's a bit dated.

There are plenty of senses in which infinity IS a number -- or rather, many numbers. See e.g. the Wikipedia articles on cardinal numbers, ordinal numbers, hyperreal numbers, and surreal numbers.

Primes ARE fundamentally predictable, in the following very strong sense: There is a deterministic polynomial time algorithm for checking whether a number is prime (i.e. the runtime is polynomial in the number of digits of the number being tested.) http://en.wikipedia.org/wiki/AKS_primality_test

Careful -- because R is uncountable, there is no system for representing arbitrary irrational numbers with finite strings. All irrational numbers with periodic continued fractions are quadratic irrationals, i.e. they can be written as A + B sqrt(C) where A, B, C are all rational. And of course, that formula immediately provides a much more straightforward way to represent such irrational numbers by finite strings!

Could you please explain why you think this guy's questions are stupid? They seemed like good questions to me. His son's school's definitions of "fact" and "opinion" seem to not be mutually exclusive, which seems to contradict the implicit assumptions in the exercises assigned to the students.