Conway chained arrow notation
Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. . As with most combinatorial notations, the definition is recursive. In this case the notation eventually resolves to being the leftmost number raised to some (usually enormous) integer power. Definition and overview A "Conway chain" is defined as follows: Any positive integer is a chain of length . A chain of length n, followed by a right-arrow → and a positive integer, together form a chain of length . Any chain represents an integer, according to the six rules below. Two chains are said to be equivalent if they represent the same integer. Let denote positive integers and let denote the unchanged remainder of the chain. Then: An empty chain (or a chain of length 0) is equal to The chain represents the number . The chain represents the number . The chain represents the number (see Knuth's up-arrow notation) The chain represents the same number as the chain Else, the chain represents the same number as the chain . Properties A chain evaluates to a perfect