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MathGroup Archive 1998

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Re: Re: Re: warning for Round[Log[2]/Log[4]]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13997] Re: [mg13950] Re: [mg13940] Re: warning for Round[Log[2]/Log[4]]
  • From: Wouter Meeussen <eu000949 at pophost.eunet.be>
  • Date: Sat, 12 Sep 1998 16:59:20 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

George,

you are right.


You are also 'lucky' : I checked if N[Log[n]/Log[n^2]] ever produces a
floating point number 'sufficiently far from 1/2' to cause the "round
to even" rule to fail:

In[ ]:=Table[Round[N [n+Log[2,n
]/Log[2,n^2]]],{n,2,4000}]~Cases~(_?OddQ) Out[ ]={}

so it holds for the first 4000 integers. The bets are open for the
lowest n where this fails.

wouter.


At 15:06 11-09-98 -0400, George E. Hrabovsky wrote:
>When I do Log[2]/Log[4]//N I get 0.5, when I do Log[2]/Log[4]//N//Round
>I get 0.
>
>	George
>
>----------
>> From: Ronald Bruck <bruck at math.usc.edu>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>> To: mathgroup at smc.vnet.net
>> Subject: [mg13997] [mg13950] [mg13940] Re: warning for Round[Log[2]/Log[4]]
>> Date: Tuesday, September 08, 1998 1:52 AM
>> 
>> In article <6ssvo6$m9r at smc.vnet.net>,
>> Wouter Meeussen  <eu000949 at pophost.eunet.be> wrote:
>> >** this is not a bug report ***
>> >  Windows 3.0.0.0.  
>> >
>> [That Mathematica didn't have enough precision to compute
Round[Log[2]/Log[4]]
>> 
>> Hmmm.  Interesting.  Since Log[2]/Log[4] = 1/2, Mathematica can't decide
>> whether to round up or down--it SHOULD apply round-to-even, to give
>> zero, but it's trying to do this with just numerical values.
>> 
>> As I recall, deciding when A == B is a profoundly difficult problem. 
>> I'm not sure how else one could go about this.  (Oh, sure, the
>> immediate problem could be fixed by applying a special rule for
>> logarithms, but what about special functions for which the relations
>> are still undiscovered?)
>> 
>> --Ron Bruck
>
>
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be



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