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When I try to buy something using bitcoins, how does that merchant know that I have payed them the agreed amount.
In other words, how does the merchant know that I payed for the product, and that they can start shipping the product to me. I thought that bitcoin was anonymous in its transactions
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These are just my supposition, but I think the merchant itself would not be bothered if someone else send the right amount to the merchant Bitcoin address :)
Since you have registered for buying the object, and the merchant sees that the amount has been received (and confirmed) in the address specifically generated for this deal, he will just conclude that it was you who paid and ship the product.
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because they most likely generated a new address for you to send your payment to. Since you're the only one that was given that address, when the payment comes in for that address, they know it was you that paid it.
Actually, Bitcoin is pseudonymous (you interact with the network through your addresses, which are observable). At any point where anyone else gains knowledge of your ownership of an address, you potentially become identifiable. E.g. when you trade fiat for bitcoin or when you use bitcoin to buy thing online that will be sent to your address. – Murch – 2013-10-17T14:02:57.377