I understand that running a full node for Bitcoin is not like running a node for other altcoins that pay you a small amount
With altcoins, you run nodes in their Proof of Stake network and get staking rewards.
during that process I wondered if anyone running a full node can confirm any Bitcoin transaction in a block even if they do not receive the gas fee? Is it necessary for the transaction to be confirmed by a miner?
Transactions confirm by miners because miners do the math and solve blocks. You can run a full nodes without ASICs which are used by miners to mine Bitcoin blocks and confirm transactions.
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