Banach Space

A Banach space is a mathematical structure used in advanced math, particularly in functional analysis. It’s a set of functions or sequences equipped with a way to measure their size or length, called a norm. Importantly, every sequence that gets closer and closer to a limit within this set actually converges to a point inside the set—this is known as completeness. Think of it as a space where you can do calculus or solve equations involving functions, knowing that limits and processes behave consistently without "escaping" the space.