|examines the behavior of a function at an infinity 'limit'|
The examination of a function at a limit, oft helps understand the nature of the function-- for some functions it discovers a paradox, for others a proof ... In the infinity case where there is no finite limit, it borders on calculus ... (One example was used in my project Sesquatercet screenplay, StarTrails, to bring a pre-highschooler up to NASA-competitive-level for solar system space exploration).
We'll look at some 'curious-to-interesting' examples:
EXAMPLE #1. "A pound, at sea level, weighs a pound." (assuming the same sea)
Suffice it to begin, we a priori expect that if a pound at sea level weighed aught differently at the equator compared to at the north pole, water would flow to make up the difference, to "reach equilibrium", (or if you live in one of my favorite trance music countries, "reach equiribrium", humor intended, as musicians do, or if you had my college professor in Advanced Calculus, as mathematicians do).
Oddly this is not commonly understood worldwide, e.g. the value of a pound is defined at 45° (North) latitude, as if latitude were a factor of some importance...
Okay, So-- to use an 'infinity comp' proof on this:
Begin mathematically with an infinitesmal mass,
Set in a massless boat of 1-square-meter area,
And note that it sinks an infinitesmal depth,
Its weight displacing equally infinitesmal water,
And, the pressure is infinitely uniform.
Subtract the water and an infinitesmal red herring. (i.e. excess explanation given for humorous effect)
If the experiment is done at a different latitude, the result is the same, because, the initial mass and displaced mass are the same.
So the depth is the same, infinitesmal,
And the pressure is the same, infinitesmal.
If the pressure were different, water would flow from one latitude to the other, until it reached equilibrium. (This would be by constant flow in the awkward case of doing the experiment near the mouth of a freshwater river.)
How does it equalize weight?-- The sea level up North is closer to the center of the Earth mass, and whence gravity is square proportionally one-factor greater, but, the other one-factor is the mass of the Earth beneath, is less: mutually compensating.
This article was developed in support of a project Sesquatercet movie-story.
A premise discovery under the title,