Regardless of your early surrounding or schooling background, we know for one that there are two kinds of mathematical objects that are kind of hard to miss in life. The names? Polynomial and Infinity! While the former might have sounded a bit like the name of a snake, polynomials is a one-of-its-kind mathematical entity whose perfection defies our mathematical imagination.
For one, polynomials are well-known for being infinitely smooth and never-ending, while at the same time, they could be a line, a parabola, or any kind of weird, infinitely-malleable curve ready to assume any shape drawn without lifting the pencil (kind of). Heck, polynomials are a favorite object of platonic desire among math enthusiasts. Talk about the interaction between polynomial and infinity!
So with all that goodness, it makes sense for us to inquire a bit as to why despite of having similar forms, the behaviors of polynomials at the infinities differ, leading to some seemingly-unrelated insights about their properties in general.
All right. Enough said. Time to buckle the seat belt, and let the theoretical musing begins! 🙂 More