Technology

You're kind of right but also very wrong. You can't convince the other ledgers that there is money in an empty wallet because all of the money in the whole system is known about. In Bitcoin every single transaction is known, every time a new coin is known. Not just by one or two people, but by every other full bitcoin instance in the entire system.

What you can actually do is something called a 51% attack. This allows you to spend money you do indeed have multiple times over. It's called a 51% attack because you need at least 51% of the processing power of the entire network under your direct control. So basically it's like cheating people by buying 51% of a bank and using that control to do dirty dealing. Actually getting to that point is incredibly hard unless you're a very rich state actor or something. At that point you might as well not bother and just mine like crazy instead of cheating the system and risk getting caught. Someone who has 51% of the processing power of the system would also get the majority of coins mined for themselves. I've seen attempts at a 51% attack but they only really work on small cryptos and even then it's very unlikely to succeed and go unnoticed for long.