Theorems Guaranteeing Fixed Points
There are numerous theorems in different parts of mathematics that guarantee that functions, if they satisfy certain conditions, have at least one fixed point. These are amongst the most basic qualitative results available: such fixed-point theorems that apply in generality provide valuable insights.
Read more about this topic: Fixed Point (mathematics)
Famous quotes containing the words fixed and/or points:
“To find the length of an object, we have to perform certain
physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined.”
—Percy W. Bridgman (18821961)
“Its my feeling that God lends you your children until theyre about eighteen years old. If you havent made your points with them by then, its too late.”
—Betty Ford (b. 1918)