Re: [math-fun] There must be something wrong with Mathematica's Round function--
Half-integers are rounded to the nearest even integer. Sincerely, Adam P. Goucher http://cp4space.wordpress.com
----- Original Message ----- From: Eugene Salamin Sent: 12/06/13 05:11 PM To: math-fun Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
Now you've uncovered an actual Mathematica bug. If Round handles 5's consistently, Out[9] should be 10, not 0.
-- Gene
________________________________ From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Sent: Friday, December 6, 2013 2:10 AM Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
MBGreen>The question still seems likely to confuse 4th graders. "How to use rounding to estimate ..."? What would the kids say if we gave them almost the exact same problem immediately afterwards, but added 2 days to both the United State and Italy numbers. I'm sure they'd expect the estimate of the **difference** to remain the same...
Right. Next time I see him, I'll do this to the poor kid: In[9]:= Round[45, 10] - Round[35, 10]
Out[9]= 0
In[11]:= Round[35, 10] - Round[34, 10]
Out[11]= 10
Also, where do they say 10 anywhere? Why not
In[18]:= Round[42, 100] - Round[13, 100]
Out[18]= 0 ? --rwg
On 2013-12-05 17:49, Bill Gosper wrote:
Oops, logophagy time. Docfiend NeilB points out: In[5]:= Round[42, 10] - Round[13, 10]
Out[5]= 30
is almost certainly the question's intent. --rwg
On Tue, Dec 3, 2013 at 11:12 PM, Bill Gosper <billgosper@gmail.com><billgosper@gmail.com>wrote:
It has no effect on this 4th Grade homework problem: "Estimate: Workers in Italy receive an average of 42 vacation days per year. Workers in the United States receive an average of 13 vacation days per year. Explain how to use rounding to estimate how many more vacation days workers in Italy receive each year." --rwg Another nice one: "Write 47,000 in expanded form." I suggested forty-seven Ms. This is a private school. Everybody says parTISSiple. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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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.
http://en.wikipedia.org/wiki/Rounding#Round_half_to_even On Fri, Dec 6, 2013 at 11:44 AM, Dan Asimov <dasimov@earthlink.net> wrote:
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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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Isn't that the IEEE floating point method for rounding the LSB? --ms On 2013-12-06 13:44, Dan Asimov wrote:
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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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.
participants (5)
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Adam P. Goucher -
Dan Asimov -
Eugene Salamin -
Mike Speciner -
Mike Stay