To OP - of course they exchange numbers. That's why it is a DIGITAL currency. If they exchanged something other than numbers, it would be analog.
I read op post and have discovered quiet a lot of things and I have arrived at a conclusion that ops is not ready to unlearn what he think and believe about Bitcoin and it creator Satoshi Nakamoto and ops havhase continually defended his point without making out time to read and absorb the views and data presented by others. That been said
What make Bitcoin real is:A: Bitcoin is transferable from peer to peer
B: Bitcoin transactions is verifiable using the transaction ID on blockchain.
C: Bitcoin have a dollar value on exchanges
D: Bitcoin is decentralized that is Bitcoin does not have a central control and that is why it is a public ledger.
If with all this facts can not convince ops of the true nature of Bitcoin than I will leave ops to believe whatever he want to believe.makes
Nakamoto disagrees with you. In the Whitepaper they defined bitcoin as a chain of digital signatures. That chain is recorded as a common record and freely available to everyone. Nobody transacts with it. It has no dollar value. That what you call a transaction is attribution of numerical value to an address and adding of it to the chain. It's just playing with numbers, not transacting.