User:Rick Wood/limit (mathematics)
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The concept of the limit is essential to the study of calculus. Without it, some people might actually be able to pass calculus, leading to the kind of degenerate grade inflation and student humping in the sciences that has currently corrupted the arts to such an extent that nobody can read without moving their lips, and poetry is dead, but don't get me started on poetry, it gives me this terrible pain down all the diodes (section removed for copyright violation).
The study of the limit, one of the three big time operators (BTOs) in calculus, usually occupies the first third of Calculus I, and then disappears, never to be seen again, until the last chapter in Calculus II, which nobody has time to get to anyway, because you have to teach the Freshman arithmetic these days, because education is dead, but don't get me started on the state of modern education.
edit A layman's description of the limit
Suppose, for example, that you have a coed in your office, and she gets down on her knees and begs and begs that you give her a passing grade in calculus, and says that she will do anything, anything you ask, in order to get a passing grade. Then, the best advice if you find yourself in a situation like that is to go the limit. Coeds today have no morals, anyway, and lose their virginity at thirteen to some pimply-faced lout who dropped out of high school when he was twenty-five, but don't get me started on the morals of today's students. They haven't any.
edit A technical definition of the limit
The limit could not exist without the greek letters epsilon and delta. Technically, we start with a function, which we call f, and if you don't know what f stands for then go back to college. We want to evaluate that function at a place called x, as in x marks the spot on old pirate treasure maps. But don't get me started on pirates.
Now, for every epsilon, there is a delta, and there exists a delta for every epsilon. Every delta is smaller than every epsilon, and every epsilon is smaller than every delta. Each is smaller than the other. Can you dig it? No? Then that's because I have a Ph.D. and you don't.
Now, we are in a position to define the limit of f as it approaches x, looking, no doubt, for the pirate treasure. We say the limit is L ifffffffff (if and only if and fuckit fuckit fuckit fuckit fuckit fuckit fuckit) (a notation due to Paul Halmos upon hitting his tumb with a hammer) every epsilon is less that every delta and every delta is less than every epsilon and all of them are really really small except when they are really really big, only bigger.
edit Funny ha ha or funny peculiar
An immediate consequence of the definition of the limit is the classification of limits into two kinds, limits that are funny ha ha and limits that are funny peculiar. Limits that are funny ha ha are easy. To evaluate such a limit, insert a male plug into a female socket and jerk off with all the other engineering majors, who get off on stuff like that. In contrast, limits are funny peculiar if they involve division by zero, which is forbidden, and can get you five to ten in Levenworth or, as Groucho Marx said...but you know that joke already. So, unless you want to serve time with a horny three-hundred-pound gorilla who is doing time for going faster than the speed of light, don't divide by zero without taking the limit first.
edit An open question in mathematics
Mathematicians have speculated for years about the existance of limits which are both funny ha ha and funny peculiar. Pierre Fermat once scribbled in the margin of a notebook, "Fuck Andrew Wiles", but that has absolutely nothing to do with the subject at hand. The best candidate to date for a limit that is both funny ha ha and funny peculiar is the limit of a function which is defined as being zero on every number divisible by three and three at every number divisible by zero. However, since mathematicians are timid creatures, and never break the law against dividing by zero, this function has never been investigated fully.
- Sir Isaac Newton, I Got Along Perfectly Well Without Limits, You Can Too, Cambridge University Press, 1671. ISBN 0520088174
- Paul Halmos, Why I Wanted to Hit my Thumb with a Hammer, Springer, 1993. ISBN 0387900926
- Freshman on Her Knees, How Can You Be So Naive, Professor Halmos, Lancer, 1959. ISBN 0861300165