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I've read that calculating how much Bitcoin you have in your wallet is going through the ledger and computing who has given Bitcoins to you and who you have given Bitcoins to. Correct me if this statement is wrong. So when a miner mines a block and earns Bitcoins, who is giving them to him (i.e. what does the transaction look like on the ledger)? Is each Bitcoin some kind of unique identifier (like a number)? If that's true, what's to prevent someone else from stealing his Bitcoins by figuring out what this identifier is?