Been lurking here a bit, finally decided to sign up. There's some gap in my understanding of how bitoins work. I hope it's OK to ask here. Here it is:
1) In the real world, if I own $100 cash, I have one piece of paper with $100 written on it that proves this fact. In the bitcoin world, I don't have a piece of file that proves my ownership of some BTC, but rather there's a peer-to-peer network that traces all bitcoin transactions and tallying some of these transactions proves how much BTC I own. Is my understanding correct?
2) If I'm correct above, then would it take longer and longer to compute who owns how much BTC as more and more transactions have taken place?
Apologies if the above questions sound stupid. I've spent hours reading and even watching videos on how bitcoin works but alas I'm not a crypto or maths expert.
Welcome.
In Bitcoin word, you can spend coins from address if you known private key, very similar, except you cant spend Bitcoins that doesnt exist.