One Broker signed the following deal with Mefistofe- les: at the beginning Broker receives ten thousands dollars in any types of banknotes. After that at each day the Broker has to pay to Mefistofeles one banknote, but can ask in exchange for any finite amount of banknotes of smaller denomination (for example, Broker can pay $5 and receive 1000 of $1 bills, etc.) On the day when Broker wont be able to pay, he loses. Show that Broker always lose (assume that all the characters live forever).