Lost coins only make everyone else's coins worth slightly more. Think of it as a donation to everyone.

With e-currency based on cryptographic proof, without the need to trust a third party middleman, money can be secure and transactions effortless.

Think of it as a cooperative effort to make a chain. When you add a link, you must first find the current end of the chain. If you were to locate the last link, then go off for an hour and forge your link, come back and link it to the link that was the end an hour ago, others may have added several links since then and they're not going to want to use your link that now branches off the middle.

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The solution we propose begins with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post. The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each additional timestamp reinforcing the ones before it.

To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back's Hashcash, rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash begins with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.

Eventually at most only 21 million coins for 6.8 billion people in the world if it really gets huge.

But don't worry, there are another 6 decimal places that aren't shown, for a total of 8 decimal places internally. It shows 1.00 but internally it's 1.00000000. If there's massive deflation in the future, the software could show more decimal places.

Right, the difficulty adjustment is trying to keep it so the network as a whole generates an average of 6 blocks per hour. The time for your block to mature will always be around 20 hours.

Long before the network gets anywhere near as large as that, it would be safe for users to use Simplified Payment Verification (section 8) to check for double spending, which only requires having the chain of block headers, or about 12KB per day.

It's very attractive to the libertarian viewpoint if we can explain it properly. I'm better with code than with words though.

Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model.

The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.