User:Rick Wood/sandwich theorem

The sandwich theorem is one of the most important theorems in that branch of mathematics known as calculus or "torture the Freshmen". Calculus is hard. No, really. Calculus is really, really hard. And of absolutely no use to anyone. Well, actually, it is essential to such disciplines as physics, chemistry, medicine, engineering, computer science, writing for the New Yorker, and torturing Freshmen, but it is of absolutely no use outside of that.

Within calculus, the sandwich theorem is a particularly useless theorem. It purports to convince students of the existance of certain limits, such as the speed limit on I-95 between Baltimore and the Shitfields of New Jersey, but in fact, since nobody obeys speed limits anyway, the theorem is, as stated, absolutely useless.

Layman's explanation of the theorem

"f, g, and h"

Bring three students to the front of the class, two large males and one small female. Have them take off all of their clothing. Place the female student between the two large males and give them each a sign to hold, the signs reading, from front to back: "f", "g", and "h". The "f" stands for "Freshman", the "g" stands for "girl", and the "h" stands for "humping the girl from behind". Now that you have the undivided interest of the class, you may proceed to explain the sandwich theorem as follows.

"Imagine," (you say), "these three young people out for a night on the town. They consume large quantities of Tree Frog Beer and are wending their happy way home at three in the morning. Now, they may wander and stagger all over the place, but -- and this is the important bit -- the girl is trapped between the two guys. She can't get out from between the two guys. No way. Now -- follow along with me closely here -- suppose the guy in front is going to a place we will designate by the letter 'L', for limit. And the guy in back, he's going to the limit, too. Now, if the guy in front is going to 'L', and the guy in back is certainly going to 'L', why the girl in the middle is going to 'L', too."

This simple layman's explanation of the theorem is usually vivid enough to cement it in the minds of the Freshmen until the next test, or the next beer bash, whichever comes first.

A more technical statement of the theorem, with proof

The sandwich theorem: Lucky Pierre! He is always in the middle!

Proof:: Let x be a sandwich. Divide the sandwich into three parts. Call the parts the Father, the Son, and Lucky Pierre. Arrange the parts in alphabetical order. The desired result follows.

References

• Martin Luther King, The Sandwich Theorem, the Most Useless Theorem in Mathematics, University of Alabama Press, 1957. ISBN 0449213358
• Steven Kranz, Why ISBN Numbers Cannot be Consecutive, Princeton University Press, 2006, ISBN 0449213359