Proposition Infinity is the fourth episode of the sixth season of Futurama. It was first aired as the fourth episode of the seventh broadcast season by Comedy Central on July 8, 2010.
The episode begins with a news report of a vandalism spree started by Bender, which ends with Bender being arrested. While bailing Bender out of jail, Amy flirts with several inmates. Infuriated at her obsession with “bad boys and paranoid that she might cheat on him with one of the inmates” Kif breaks up with her. The break up severely upsets Amy, and to make her feel better, Leela, Fry, and Bender take her to Forbidden Planet Hollywood. Bender mocks her all night, insulting and infuriating her. They end up in bed. After this, Amy and Bender discover a mutual attraction for each other and enter into a robosexual relationship, which is taboo in 3010, so they keep quiet about their relationship, even to their friends and co-workers. The co-workers grow suspicious, but think nothing of it.
While at the planet Tornadus, collecting tornado wind for the Professor's entry for the county fair, the crew is shocked to learn that Bender and Amy are missing. They discover their clothes flying around in the tube with the tornado winds, so the Professor shuts off the machine, and when the winds go away, the crew is shocked to see Bender and Amy making love. Discovering this, the Professor immediately disapproves of it. The rest of the crew accepts Bender and Amy's relationship, which they thank them for, as she knows her family will disapprove. The professor informs Amy's parents of the relationship, then calls Reverend Preacherbot for Bender. While at her parent's ranch, Amy is saved by Fry, who poses as her new beau to get her parents off her back. Amy saves Bender from the camp that Reverend Preacherbot sent him to. They go back to the Planet Express building, where Bender proposes to Amy. The Professor reminds them that robosexual marriage is illegal in New New York. To fight against this, Bender and Amy launch a campaign for the legalization of robosexual marriage.
They launch Proposition ∞, which, in days before the election, slumps in the polls. Amy loses hope, but Bender says that they will win due to his upcoming debate against Professor Farnsworth, the leader of the Prop ∞ opposition. At the debate (moderated by the head of George Takei) Bender gives a heartfelt speech, which the audience applauds. The Professor follows with his rebuttal, saying that he was in love with a fellow scientist named Eunice, and, 43 years later, discovers her in bed with a robot. This does not impress the audience and Amy confronts the Professor for his hatred of robosexuals because his losing his girlfriend to a robot. However, he admits that she was actually a robot, named Unit 47, who slept with another robot. Farnsworth's heart was broken, so he took his anger out on other robosexuals. After admitting the truth, the Professor withdraws his argument, fully in support of Prop ∞. The next day the proposition is approved. Amy is ecstatic, saying that she and Bender can have a normal, monogamous marriage now. Bender then leaves Amy for two robot hookers, while Amy goes back to Kif, who assumes a bad boy persona for her.