"Inf" is an in-game measure of currency in the world of the City of Heroes MMO. "Inf" is short for three different currencies:
"Influence" is the established currency for registered heroes in Paragon City. Since some heroes did not need money, and others still felt guilty for being paid for doing heroic deeds, a credit system was established where recorded actions are rewarded with a credit system. This credit system can be used in certain businesses in Paragon City, or it can be exchanged for paper currency.
"Infamy" is the currency for recognized operatives and Arachnos agents in the Rogue Isles. Set up during a time of economic recession for the Isles, Lord Recluse created the credit system to keep his Arachnos soldiers from deserting their posts. Then, during the great recruitment known as Operation DESTINY, the system was extended to the new operatives.
"Information" is the credit system for operatives in Praetoria. Emperor Cole set up the credit system for his Powers Division heroes during the early years of Praetoria prior to the establishment of the Merit system.