Imagine a "grid" of people: some number of people arranged in a number of rows and columns in a rectangular formation.
We designate person A as the shortest person in the group of the tallest people of each row. We then designate person B as the tallest person in the group of shortest people in each column.
Who is taller, A or B?
(In reply to Four line proof:
by G. Steve Arnold)
Actually, what you proved is not really more general, since the more general case must be true if the specific csae is true. If A is The shortest of the tallest from each row, then any of the others Tallest in their row must be taller than A. Since A is taller than B, then any of the others is taller than B. Likewise, A is taller than B, who is taller than any of the other "shortest." So any "Tallest" is clearly taller than any "shortest" (Assuming no two persons are the exactly same height, and A =/= B, neither of which has been ruled out -- showing that your use of ≥ instead of > was a wise precaution)
While the more general case is true, it is the specific which is more interesting, since it shows that the first designation (tallest in the row, shortest in the column) determines more strongly than the second (shortest of the tallest, tallest of the shortest.
Posted by TomM
on 2002-07-10 03:42:40