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I understand that the main purpose of the mining process is to maintain the network and protect it from fraud.

However, every transaction is signed by the sender's private key, and then it's verified by the network (the other nodes) using the sender's public key.

Isn't that enough to protect the network from fraud and cheats? Even if there is spam with many invalid transactions, the verification is a light operation, and they can be immediately detected and rejected.

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