We can also know that transaction amounts are valid even though the value of the inputs that you are spending and the value of the outputs you are sending are encrypted (these are hidden to everyone except the recipient). Because the amounts are encrypted using @Pedersen-commitments what this means is that no observers can tell the amounts of the inputs and outputs, but they can do math on the Pedersen commitments to determine that no Monero was created out of thin air.
We can also know that transaction amounts are valid even though the value of the inputs that you are spending and the value of the outputs you are sending are encrypted (these are hidden to everyone except the recipient). Because the amounts are encrypted using @Pedersen-commitments what this means is that no observers can tell the amounts of the inputs and outputs, but they can do math on the Pedersen commitments to determine that no Monero was created out of thin air.
