Just got my question thrown out of SO. Trying to find a loving home for it. Here it is, just for context (will delete it if it is also inappropriate here, don't sweat it :)
I'm trying to understand the concern that bitcoin's chain of blocks technique tries to solve (see http://www.bitcoin.org/bitcoin.pdf). Warning: not a crypto-dude, be tolerant.
I understand that basically we're worried about "double spending". I'm able to grasp this idea when talking about discrete, indivisible coins. E.g. there are only 3 coins in the world, which cant be divided to cents, and we need to track the history of all 3, and to make sure that each payer really had the coin he claimed to have while paying with it.
While I'm able to see how this concept extends to millions of coins, I can't get how does it extend to fractions of coins. How does a "double spending" attack scenario actually looks like? how do the honest nodes scrutinize a nominated new block, after some node proposes it as the new head node? please provide me with some illustrative examples...