So I'm watching a video where Andreas Antonopoulos explains how bitcoin transactions are structured. I think I understand the input side (the spending side), and I think I understand the output side (the recipient address and the change address). But I'm confused about the transaction fee paid to the miner.

Andreas says the input side (eg, 100,000 satoshi) will not be equal to the output side (eg, 98,000 satoshi). He said the difference is the transaction fee paid to the miner (2,000 in this example), but this fee does not appear in the transaction.

If I understood Andreas correctly, I'm confused about this. Doesn't the transaction fee need to go to the miner's public bitcoin address? If it's not specified in the transaction (as an output), where is it? I assume it must be somewhere on the blockchain?

Thanks.