The Solution Set : Slide 1

Physicists are no good in mathematics, American analysis, nor at making lots of money. My background was physics, and as such, I learned some of the basic tenets of physicists. We do have some fundamental rules, however. Two numbers that are very popular with us are "zero" and "infinity". These manifest themselves in theories such as the Big Bang, Quantum Mechanics and Black Holes. We generally like to think in terms of limits. In other words, "one" out to the infinite comes back to zero. Therefore, those are the only two points of interest. Anything else are details for engineers and chemists.

Spring in New England brings blackflies. These blackflies are ubiquitous and tenacious. Walking outdoors for the two to three weeks they exist is impossible. Recently, I built a barn for my work at home. On the third floor of this barn there is an open deck. The deck was not screened because I knew that no mosquitoes or blackflies would be present on the deck. How did I know? The way it works is, I know there is an infinite number of mosquitoes and black flies on the ground during certain times of the year: "infinity". I also know there are no mosquitoes and blackflies on the moon: "zero". The reasons are details. The fact is, that in those two limits, it describes the boundary set for the existence of all mosquitoes and blackflies as far as it concerns the empiricist being of Morley. My deck is on the third floor and is clearly between those two limits. It is better to be on the deck that it is at either the infinity or the zero, which defines the boundaries of the sets of interest.

You really should try to remember that it is better to be between the limits than at the limits, provided the definitions are correct. We must hang onto this concept because it will be very important in the following pages.

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