John Conway also invented a mathematical notation, based on Donald Knuth's up arrow notation, called the chained up-arrow notation.

In the up-arrow notation, (a ↑ b) is to (a ^ b) as (a ^ b) is to (a * b), (a ↑↑ b) is to (a ↑ b) as (a ↑ b) is to (a ^ b), etc. Eventually, the ↑s get cumbersome, until you use the chained up-arrow notation.

For those of you with browsers that don't display the symbol properly, that ↑ is an upward-pointing arrow.

In the chained up-arrow notation, (a ↑ b) is written (a → b → 1), (a ↑↑ b) is written (a → b → 2), (a ↑↑↑ b) is written (a → b → 3), etc.

Those expressions with two terms have the ↑ up arrow symbol, the expressions with three terms have the → right arrow symbol.

(Extending this notation probably beyond what Conway intended, it could be argued that (a → b → 0) is (a ^ b), and (a → b → -1) is (a * b), and (a → b → -2) is (a + b).)