fixed points

A fixed point is a value that remains unchanged when a specific process or function is applied to it. For example, if you have a function that doubles a number, the fixed point would be zero, because doubling zero still gives zero. Fixed points are important in mathematics and science because they often represent stable states or solutions that the system tends to settle into. Understanding fixed points helps analyze how systems behave over time, such as equilibrium points in physics or steady states in ecology.