How do you make sure a sender isn't sending bogus funds?

Question

It is my understanding that RingCT allows the verifier to make sure that the sum of the inputs is the same as the sum of the outputs in a transaction, so that no monero is magically created or lost. All while hiding the actual amounts.

However, in the event where the sender would be giving more monero than his balance, how is that detected by the network ?

Answer 1

If the sender would be giving more monero than his balance,

In this event, he can't sign the transaction because the actual transaction input (P,C) is previous transaction output someone sent to this sender and (P,C) was recorded by blockchain.

P is the stealth address, C contains the amount.