Nice. These problems are circumvented by the use of an odd radix, such as ternary (base-3). Balanced ternary has the beautiful property that rounding and truncation are precisely the same operation, and it's very easy to represent and compute negative numbers. I seem to recall that the Russians even had a balanced ternary computer in the mid-20th-century, called Setun or something like that. Sincerely, Adam P. Goucher
----- Original Message ----- From: Eugene Salamin Sent: 12/06/13 07:05 PM To: math-fun Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
Every system of rounding has some arbitrary convention for dealing with 5. I like the convention that was used in numerical tables, in which a least significant digit of 5 that was rounded upward had an overbar over the 5 to signal that the number should be rounded downward in a further rounding. For example, the number 0.12349 in a 4-place table is written as 0.1235 with an overbar over the 5. Then if someone wants a 3-place value, they know to use 0.123 rather than 0.124.
-- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, December 6, 2013 10:44 AM Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
OK, that would explain Mathematica's reasoning.
But why? According to what system of rounding?
--Dan
On 2013-12-06, at 9:36 AM, Adam P. Goucher wrote:
Half-integers are rounded to the nearest even integer.
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