Motivation: It is well known that Super Mario Brothers is a game series that is defined for all positive real numbers. We are interested in determining how the games act for large values in the series.
We already know that as Mario approaches a Goomba the series is bounded by the function of one over two to the power x. Mario; therefore, approaches zero for non-trivial Marios (i.e. Mario with a star).
Other behavioural patterns found by Mario is that Mario is always greater than Luigi. For every Luigi, there exist at least 3 times as many Marios. So if Luigi is less than δ we cannot find an ε such that Mario is less than ε for all Luigis. For all values of Marios, the Mushroom is the inverse of the Goomba.
We can determine Mario's multivariate behaviour by using the Yoshi matrix transformation. However, the Yoshi has the long-run behaviour of the single state: the egg state.
Further analysis for the Super Mario Brothers is a growing branch for graduate studies in Pure Math. See your professor for details, and shortly after receive a mark of 32.