Conway chained arrow notation: Difference between revisions

Revision as of 07:43, 26 July 2025

Revision as of 13:59, 26 July 2025

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A "Conway chain" is defined as follows:

* Any positive integer is a chain of length <math>1</math>.

* A chain of length ''<math>n''</math>, followed by a right-arrow → and a positive integer, together form a chain of length <math>n+1</math>.

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 <math>a, b, c</math> denote positive integers and let <math>\#</math> denote the unchanged remainder of the chain. Then:

#An empty chain (or a chain of length <math>0</math>) is equal to <math>1</math>.

#The chain <math>a</math> represents the number <math>a</math>.

#The chain <math>a \rightarrow b</math> represents the number <math>a^b</math>.