An answer to your first question: Basically, when you receive X amount of BTC, that transaction is recorded on the public Bitcoin ledger. This ledger is shared throughout the network; there are thousands of copies. The ledgers are verified using a cryptographic hashing algorithm. Therefore, the system knows that you own X amount of BTC because it is recorded on the public ledger, which is unhackable. 2nd question: yes it does still apply. This is because you still have the same amount of BTC in circulation. For example, you can divide the number 1 into 2 halves (0.5, 0.5) or quarters (0.25, 0.25, 0.25, 0.25) but in the end, it still adds up to one: 0.5 + 0.5 = 1; 0.25 + 0.25 + 0.25 +0.25 = 1. Therefore, the scarcity isnt affected.