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So far I thought that mining is the process, when the network verifies transactions. When a transaction is verified, it gets added to the blockhain. In other words, a new block has been found. Then the miner, who found the block, will be rewarded with some Moneros, in the expenses of the sender.

After checking a few blocks it seems to me that the network "prints" and gives away free Moneros for each participating miners, who do nothing but wasting CPU cycles or consuming electricity.

Could someone explain it, what are the miners doing when there is nothing to verify? And what is the benefit of giving them Moneros for that time?

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the miner, who found the block, will be rewarded with some Moneros, in the expenses of the sender.

That also happens, and it is called a transaction fee. Transaction fees are small: 0.002 XMR (per output, or Kb, I am not sure).

On the other hand, what you are observing is the block reward of about 10 XMR per block found which seems wasteful at first glance, but that is what is known as proof of work, and it is what allows decentralization to happen. The point being: the network wants to maintain the integrity of the record of transactions known as blockchain, but if people can edit it at will that is not possible. So the solution, which was Satoshi's real stroke of genius was to create this block reward which works as a lottery in which your chances of winning are proportional to the resources you have invested (hardware plus electricity). The end effect is that it is hard for any agent to get the privilege of editing the blockchain, while at the same time aligning their interests with that of the network, since they only get the reward if they edit the blockchain according to the rules, and also the very coins they get in return derive their value from the integrity of the blockchain, which therefore they should work to protect. It is circular, I know, but it works for bootstrapping currencies.

It is worth noting that those moneros that the miner gets therefore are not "free" since they have to win the lottery, but yes, that is the cost we pay to secure the network. It might seem wasteful, until one notices that physical security of a bank, for example, also cost a lot: building the vault, paying the guards, setting up alarm systems, securing their own networks and databases etc. So when talking about costs it is important to ask: "compared to what?"

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