I'm reading about the concept of UTXO. Everywhere I read, it says that a UTXO in an account is indivisible. One analogy said: "It's as if you wanted to make a $5 purchase with a $10 bill. You wouldn't tear the bill in half."
Let's say I have 0.1 BTC as one coin in my wallet and I want to send 0.05 to someone. What I'd do (minus the fees) is send 0.05 to the person and 0.05 coin back to myself, right? That is, it will be marked in the coin's ledger that I and they respectively are assigned that fraction of it. At the moment of the transaction, wouldn't the coin be split?
Also, at the moment of original mining, aren't all new coins worth 1 BTC? If that is that case, they must be split in some way at some point. Otherwise, the amount of bitcoin that people own in the world would all be integers.