2-4-6.5 : Donald Knuth's illion Scheme

Donald Knuth's -illion Scheme

Donald Knuth, who is also the creator of up arrow notation, has invented an "-illion scheme" that is quite unique for a few reasons. Noting the inefficiency of name usage in the standard -illion schemes he suggests something much more extendable. What that means will become clear shortly.

First of all, his system is not technically what I would call an "illion series" in that his numbers are not powers of a thousand but rather powers of a myriad, which is 10^4 or 10,000. He suggests using this as the starting term, just as the greeks had done.