Apologies, Dick, I certainly didn't mean to do so.Dick said:As Unco suggested, maybe without spelling it out completely
A fixed point in a continuous set is a point where the output of a function is equal to the input. In other words, it is a point where the function does not change its value when applied to that point.
A fixed point is a specific type of root or solution where the output of a function is equal to the input. In contrast, a root or solution can be any point where the function is equal to a given value or set of values.
Fixed points are important in mathematics because they can help us understand the behavior of a function. They can also be used to find roots or solutions to equations, which has many practical applications in various fields of science and engineering.
Yes, a function can have more than one fixed point in a continuous set. In fact, some functions have an infinite number of fixed points, while others may not have any.
Fixed points can be calculated or approximated using various numerical methods such as iteration, bisection, or Newton's method. These methods involve repeatedly applying the function to a guess or starting point until the output converges to a fixed point.