Knuth -yllion
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Donald Knuth adapted the familiar naming schemes to handle much larger numbers, dodging ambiguity by changing the -illion to -yllion.
Knuth's digit grouping is exponential instead of linear; each division doubles the number of digits handled, whereas the familiar system only adds 3 or 6 more.
- 1 to 99 have their usual names. (In fact 1–999 have their usual names, and will be used below to save space; but to emphasize the pattern, this group is separate.)
- 100 to 9999 are divided before the 2nd-last digit and named "blah hundred blah". (e.g. 1234 is "twelve hundred thirty-four"; 7623 is "seventy-six hundred twenty-three")
- 104 to 108-1 are divided before the 4th-last digit and named "blah myriad blah". Knuth also introduces at this level a grouping symbol (comma) for the numeral. So, 382,1902 is "382 myriad 19 hundred 2".
- 108 to 1016-1 are divided before the 8th-last digit and named "blah myllion blah", and a semicolon separates the digits. So 1,0002;0003,0004 is "1 myriad 2 myllion 3 myriad 4"
- 1016 to 1032-1 are divided before the 16th-last digit and named "blah byllion blah", and a colon separates the digits. So 12:0003,0004;0506,7089 is "12 byllion 3 myriad 4 myllion 506 myriad 70 hundred 89"
- etc (although what separator follows is not obvious)
Abstractly, then, "one n-yllion" is 
. "One trigintyllion" would have nearly forty-three myllion digits.
[edit] See also
[edit] References
- Donald E. Knuth. Supernatural Numbers in The Mathematical Gardener (edited by D. A. Klarner). Wadsworth, Belmont, CA, 1981. 310 — 325.
