Alternative descriptions for math concepts/neat heuristics for concepts in math?

Question

There are some cool verbal/"intuitive" explanations for laws and tricks in math that are good substitutes for the formal definitions that are often given in classroom and textbook settings. This thread is for people to share their own personal favorites or ones that have helped them in the past. For example, I like the verbal description of integration by parts as "the area under a curve over a space is equal to the total space, minus the area over the curve in the space."

Answer 1

I would say that a lot of concepts from homotopy theory fit the description. For example, you can talk of paths and loops as twines and nooses, regardless of the fact that, formally, they are continous functions.