Notes

Bitcoin transaction
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The above describes the case of each transaction in isolation. A transaction is an exchange. A bitcoin is the unit of bitcoin as the payment medium in a transaction. A bitcoin is transferred from a sender's bitcoin address to a recipient's bitcoin address. In a typical bitcoin transaction:

Sender has their bitcoin address for which they will receive bitcoin

Recipient has their bitcoin address for which they will send bitcoin

Sender sends their bitcoin to recipient over the bitcoin network through multiple intermediaries called miners.

Each intermediate entity in a blockchain is referred to as a node. Miners verify transactions and add the appropriate transaction information to their copy of the blockchain.

A transaction outputs are the bitcoins that a transaction can spend. This is defined as the transaction's change outputs minus the transaction's inputs and fee. During a transaction verification process, the miner must validate the transaction by including the inputs and outputs of the transaction into a block, as well as calculate the transaction fees due. Once this is verified, the transaction information will be added to the ledger, and a new block will be hashed and placed at the tip of the blockchain in front of all other blocks. The transaction information becomes part of the block that is hashed. This process of adding transactions to new blocks and the block itself containing transactions is called mining.

Change outputs
A transaction's change outputs are the bitcoins that a transaction can spend, minus the transaction's inputs and fee. They are the transaction's outputs. The transaction outputs are defined as the transaction outputs minus the transaction inputs and fee:

is the original outputs of the transaction,
is the original input of the transaction,
is the transaction fee, and

All transaction outputs must be collected and retained as a change output, until they have been redeemed. In a typical bitcoin transaction, a difference may exist between change outputs that were offered and change outputs that were collected. For example, a payment of 0.1 BTC for 0.9 BTC of services offered requires that:

1.1 BTC of change outputs be collected by the fee recipient,

and 0.8 BTC of change outputs remain as potential change outputs, or change output opportunity:

0.9 BTC out of 1.1 BTC are collected.

0.9 BTC out of 1.1 BTC become potential change outputs:

1.1 - 0.8 BTC, or 0.2 BTC of change outputs, become change outputs available for
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