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mathematical

There exists a pair (*r*, *x*) such that *r* is a member of the set of all restaurants, and *x* is a member of the set of patrons. There exists a unique *x* such that, for some book *b*, the relation *R(x, b)* holds, where *R(p, q)* is true iff *p* is reading *q*. Let *W* be the set of all elements *w* where *x* is writing *w*. *W* is nonempty.

The cardinality of the set of players *P* such that iff *q* is a member of *P*, then *q* is playing Scrabble in some restaurant *r* (as posited above), is 2. The probability that a randomly chosen element from this set has a puzzled expression on his face is precisely one-half.

Without loss of generality, it can be shown that there exists a glass of water *w* such that the second derivative (with respect to time) of its distance to some floor *f* is -9.8 meters per second squared. It can be shown that for all such events, if the number of waiters near the point of impact prior to the event is *k*, the number of waiters near the point of impact after the event approaches 3*k*. There exists some positive number *n* such that there exists a patron *p* where *p* offers *n* napkins to each of the 3*k* waiters.

For some positive, even, integral number of hours fewer than four later, the unique element *x* mentioned above can be shown to belong to the set *F* where if *y* is a member of *F* then *y* is a geographically proximate friend of *x*. Furthermore, *F* possesses a bijection onto the set of conversations in which *x* is engaged.

There exists a set of cars *C* such that, for any three non-colinear elements of *C* the unique plane containing the three elements contains all the points in the path defined by some known bicyclist *b*. Although continuous, the path is otherwise fundamentally chaotic.