So while I relax in the Newbie pool I'm trying to understand some of the more technical aspects of BitCoin. Over and over again we hear and read that there is a limit of 21 million coins that can ever be minted, but I'm interested in what that actually means in terms of BitCoin source code. Is this limit due to the fact that there is a variable defined with a certain bit-length limiting how high of numbers can be expressed? Or is it due to the algorithm for mining rewards where every 210k blocks the reward is halved? Something like:

50*210,000 + 25*210,000 + 12.5*210,000 + . . . ~= 21,000,000 BTC?

I've been digging through the forum and wiki and even making small forays into the source code to try to understand this, but I don't have a lot of programming or crypto knowledge. Any explanations from knowledgeable individuals would be appreciated.