How can something be infinite? Well easily if you just keep adding to it. This is the case with Bioshock Infinite due to DLC.
The first part of BioShock Infinite's latest DLC - a two part tale, is called Burial at Sea. Lo! It takes are hero/antihero Booker back (or forward) to Rapture but you don't just play the DLC has him, you also get to play as adult Elizabeth... there are also Big Daddies!! Check out the trailer below: