Editing Conway chained arrow notation (section)

==Definition and overview==
A "Conway chain" is defined as follows:
* Any positive integer is a chain of length <math>1</math>.
* A chain of length ''n'', 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 0) 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>.
#The chain <math>a \rightarrow b \rightarrow c</math> represents the number <math>a \uparrow^c b</math> (see [[Knuth's up-arrow notation]])
#The chains <math>\# \rightarrow 1</math> and <math>\# \rightarrow 1 \rightarrow a</math> represent the same number as the chain <math>\#</math>
#Else, the chain <math>\# \rightarrow (a+1) \rightarrow (b+1)</math> represents the same number as the chain <math>\# \rightarrow (\# \rightarrow a \rightarrow (b+1)) \rightarrow b</math>.