"To infinity and beyond!" was Buzz Lightyear's classic line and has seen a variety of usages. Not only on T-shirts, but among philosophers and mathematical theorists as well. Standard definition: Without limits, limitless, sky's the limit (e.g. limitless possibilities, etc.) Definition based on the Humanistic Theory: It is a catchphrase that was featured in the 1995 Pixar animated film Toy Story. Lucia Hall of The Humanist linked the film's plot to an interpretation of humanism. She compared the phrase to "All this and heaven, too!", indicating one who is happy with a life on Earth as well as having an afterlife. Definition in Mathematical Circles: What exactly does Buzz Lightyear mean when he says, "To Infinity and beyond!"? A few professionals at Harvard investigated the origin of this quote and traced it back to limits. According to Dr. Sanjay Gupta, "Buzz Lightyear is a metaphor of a funtion which approaches a certain number, but never actually reaches it." However, experts at MIT believe that Buzz Lightyear is referring to vertical asymptotes. Dr. Benjamin Hernandez says, "It is possible to cross horizontal asymptotes, but verticals are impossible. Buzz Lightyear is showing everyone that he can do the impossible and cross horizontal and vertical asymptotes."

In a sense, there is no such thing as "beyond infinity", since infinity can't be reached. In geometry however, if you go "beyond" infinity, you start coming back to your starting point from the opposite direction. Just like crossing the half-way point of a circle!

no limits

It means there aren't any limits.