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:
“Since an intelligence common to us all makes things known to us and formulates them in our minds, honorable actions are ascribed by us to virtue, and dishonorable actions to vice; and only a madman would conclude that these judgments are matters of opinion, and not fixed by nature.”
—Marcus Tullius Cicero (106–43 B.C.)
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—Willard Van Orman Quine (b. 1908)