Complexity and hyperoperations | Data Structures Math Foundations 174

We introduce the idea of the complexity of a natural number: a measure of how hard it is to actually write down an arithmetical expression that evaluates to that number. This notion does depend on a prior choice of arithmetical symbols that we decide upon, but the general features are surprisingly independent of this initial system. One important tool are higher operations that go beyond the familiar addition, multiplication and exponentiation operations: these have been called hyperoperations and have been studied by many people. Video Content: 00:00 Intro to complexity in arithmetic 3:40 Operations to include in arithmetic 5:58 A natural hierarchy of operations 8:54 Exponentiation 10:52 Additional important laws 14:54 Hyperoperations 21:18 Squarification 24:47 ’m to the square n’ 26:28 Precedence of operations 28:30 Complexity ************************ Screenshot PDFs for my videos are available at the website . These give you a