Imagine an island with two residents. Alice and Bob. There is no difference between these two scenarios:
1: Alice has 1 seashell. Bob has 0 seashells.
2: Alice has 0 seashells. Bob has 0 seashells. Bob owes Alice a seashell.
Either way, Alice can go to bob and exchange her wealth for an apple. In scenario 1, she gives him a seashell. In scenario 2, she pays by voiding his debt.
Either way, Alice owns 100% of all wealth.
3: Alice has 0 seashells. Bob has 1 seashell. Bob owes Alice a seashell.
Once all the accounts are settled by Bob paying Alice the seashell he owes her, it becomes scenario 1, so this seems a better match for scenario 1 than scenario 2 does.
What I wanted to emphasize is that a dollar "In the bank" means nothing else then "The bank owes you a dollar".
And banks do not lend money they don't have. And where do they have it from? From other customers.
Ergo: Your $1 in wealth is someone elses $1 in debt.
Supposing we had a scenario where once all accounts are settled, Alice has 2 seashells, and Bob had -1 seashells, does alice have 100% of all wealth? 200%? (Equivalently, Alice has 1, Bob has 0, and Bob owes Alice 1)
(edit for everyone else: this thread is confusing because I changed my comment to respond to founderling's edit, but founderling responded to my original comment before I changed it... ¯\_(ツ)_/¯)
Alice has 2 seashells, and Bob had -1 seashells
does alice have 100% of all wealth
Actually that is exactly what banks do. You go to the bank and take out a loan, they credit your account with $1000 and then you owe them $1000 and they owe you $1000. The thing balancing the cash in your account isn't some other customer's cash, it's the debt you owe them. The amount of physical cash in their vault as a result of you taking out the loan hasn't changed at all.
They're required to have a certain amount of cash in reserve to cover cash withdrawals, but that amount is not 100%.