Total monotonicity

Total monotonicity means that something always increases or always decreases, without any exceptions or interruptions. It's like walking up stairs - you keep going higher and higher, without ever going down or stopping. Total monotonicity is a very important idea in math, because it helps us understand how things change and behave over time. It can show up in all sorts of situations, from how fast a car accelerates to how quickly a disease spreads. When something is totally monotonic, we can predict exactly what will happen next, and that can be very useful for making decisions and solving problems.