[math-fun] "long tail" number notations?
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ? I'm particularly looking for notations which *don't* converge quickly. This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?
Roman numerals. Brent On 4/22/2018 8:53 AM, Henry Baker wrote:
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ?
I'm particularly looking for notations which *don't* converge quickly.
This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
A little Googling told me that I should be thinking about "mixed radix number systems", "change-making problems", "coin collector's problem", "implied probability distributions", and "Fibonacci codes". The Fibonacci code is particularly interesting, since the implicit probability distribution is O(n^-1.44), which is pretty darn close to the O(n^-1.5) from theoretical & empirical grounds for cache behavior. https://en.wikipedia.org/wiki/Fibonacci_coding This coding suggests that an elegant computer cache might possibly be designed using *Fibonacci numbers*. At 08:53 AM 4/22/2018, Henry Baker wrote:
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ?
I'm particularly looking for notations which *don't* converge quickly.
This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?
FWIW https://en.wikipedia.org/wiki/Factorial_number_system On 4/22/18 8:53 , Henry Baker wrote:
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ?
I'm particularly looking for notations which *don't* converge quickly.
This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .
* Andres Valloud <avalloud@smalltalk.comcastbiz.net> [Apr 25. 2018 15:47]:
Warning: in the format described the digit right of the "decimal point" is always zero. And that is just silly! Best regards, jj
On 4/22/18 8:53 , Henry Baker wrote:
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ?
I'm particularly looking for notations which *don't* converge quickly.
This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Andres Valloud -
Brent Meeker -
Henry Baker -
Joerg Arndt