Thus, in the borrowing example, Alice and Bob lose money and Christina gets it. In the BigBank example, no one loses money, but everyone trusts BigBank, and so their pledge that Christina has 2,000BTC to spend is just as good as those 2,000BTC, even though their pledge is a lie, and those bitcoins do not exist.
I routinely pay with friends' debts as currency.
"Hey, Bob owes me a hundred; when he pays he can pay for me too."
"Sure."
Businesses do similar things and without banks they would do it more. Sure, BigBank is more efficient at it but the effect is there.
That is the situation which causes inflation, and it is in no way related to the underlying supply of pieces of paper that make dollar bills, or hashed kilobytes that make real bitcoins.
So how come there has been no such inflation in gold in the hundreds of years it has been used as a currency in fractional reserve banking?
However, for 99.99% of the population, there is *no* difference between a bitcoin and a bank's fraudulent claim that bitcoins are in an account. So, no one would ever (or would very rarely) demand bitcoins, making the number that the bank had to keep on-hand far more manageable, and in fact probably just a bit above 0.
There is one important difference. If bitcoins become widespread it will be more convenient and less costly to pay with bitcoins than with bank balances. That makes the demand for real bitcoins pretty high.