Learning that such article could exist (it DOES exist), and reading it was a shocking experience to me.

'A second-year was "quite convinced" that zero was odd, on the basis that "it is the first number you count"'

Chromium is also a must.

guess 2/3 of average: http://en.wikipedia.org/wiki/Guess_2/3_of_the_average

pirate game: http://en.wikipedia.org/wiki/Pirate_game

dollar auction: http://en.wikipedia.org/wiki/Dollar_auction

Most common/well-known:

prisoner dilemma: http://en.wikipedia.org/wiki/Prisoner%27s_dilemma

chicken: http://en.wikipedia.org/wiki/Game_of_chicken

battle of the sexes: http://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theor...

El Farol bar: http://en.wikipedia.org/wiki/El_Farol_bar_problem

I'll allow myself to give some advice for those who are interested in problem-solving, but have no experience. If you have some, then this should be well known.

* Keep problem / exercise ratio as high as possible. This is impossible with many calculus books; find a book with hard problems. An "exercise" is something which checks your understanding of definitions and theorems; a "problem" is something which exercises your skill and forces to think. Do exercises if the theory is unclear. If a task starts with "using mathematical induction prove that..." then it is an exercise. A problem forces you to think how to do it.

* Doing differentiation exercises will give you some speed, but after five-twenty minutes your brain will stop thinking and start to rot. Healthy mathematics - just like programming - hates doing the same thing again. Of course you have to learn some algorithms, but this is a tip of the iceberg.

* Always take 20 minutes (some say more) on a problem, unless you think it is ill-posed; giving up early is stupid. If you think the problem is impossible, try proving it. Think about some way of solving, reject it quickly if you made a thinko; if you sense "this might work" go deeper. Use paper.

* Don't read too much on philosophy of mathematics or biographies; this isn't deep from the mathematical side. Other articles (http://www.artofproblemsolving.com/Resources/AoPS_R_Articles...) are also worth reading. Check their forum (http://www.artofproblemsolving.com/Forum/index.php or www.mathlinks.ro).

alpha direct link: http://www.wolframalpha.com/input/?i=(x-3)/(x-1)%3D(x-4)/(x-...

Bing's formatting of the results doesn't quite draw your eye to it - look for "Calculation" immediately below "All Results"

'Multiplying 0 by itself 0 times' is what Wikipedia calls 'empty product'. For me is is good intuition, but that's a matter of taste.

AFAIK the usual convention is:

* in contexts where the exponent is varying continuously and a is a real number, a^b is undefined for a=b=0

* in contexts where the exponent is varying discretely (as an integer/natural number), a^b = 1 for b=0 and any a

Haskell quite nicely distinguishes between these two:

(^) :: (Num a, Integral b) => a -> b -> a

(* * ) :: (Floating a) => a -> a -> a

but it still gives 0 * * 0 and 0^0 as 1. (There shouldn't be spaces between asterisks, HN treats them as italics)

I think his point was that 0 has no inverse. So in the literal sense, the reals are not a group under multiplication (although obviously, when somebody says "the reals are a group under multiplication", one usually interprets it as "R\{0} is a group under multiplication".)

This is vaguely relevant to the issue at hand because we are doing 0 to the 0.