Suppose I always pay for things with exact change, if I have it, or the least amount over the cost of the item(s) if I don't have exact change (in which case I'll get change from the seller).
Also, assume my source of money is $20 bills (as from an ATM).
In the boundary case, where I have exactly \$20 (possibly all in pennies, but however) and something costs exactly $20, I use the change I have. I only go to the ATM when something I'm going to buy costs more than I have.
Is it possible for the amount of change I have (the number of coins, say, not how much money the coins add up to) to increase without bound? That is, could there be some pathological sequence of prices of purchases in which the number of coins keeps increasing (overall)?