RE: Re: Re: MemberQ

*To*: mathgroup at smc.vnet.net*Subject*: [mg68695] RE: [mg68677] Re: [mg68655] Re: MemberQ*From*: "Erickson Paul-CPTP18" <Paul.Erickson at Motorola.com>*Date*: Thu, 17 Aug 2006 04:17:53 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Do you find that any stranger than the following? In[7]:= 2 == 2.00000000000000000001 Out[7]= True If you don't want Mathematica to make assumptions on your behalf, then you have to tell it exactly what you do want, as in: In[9]:= 2 == 2.00000000000000000001``50 Out[9]= False (* as in the exact number 2 isn't equal to the very accurate number close to 2 *) In[12]:= 2. == 2.00000000000000000001``50 Out[12]= True (* But the real number 2. with limited accuracy is close enough to the very accurate number close to 2 *) In[13]:= 2``50 == 2.00000000000000000001``50 (* where two very accurate close number aren't equal *) Out[13]= False In[10]:= 2 // FullForm Out[10]//FullForm= 2 In[11]:= 2.00000000000000000001``50// FullForm Out[11]//FullForm= 2.00000000000000000001`50.30102999566398 So in general, it appears that Mathematica tries to call two numbers equal if they are close compared the accuracy of the less accurate number. Some of the postings would indicate that Mathematica doesn't always succeed in this wrt MemberQ and it would appear that it may be machine dependant. Still seems best to just avoid the problem or deal explicitly with it. As to an earlier question about 2/10 vs 1/5, I think Mathematica is don't exactly what it says it should in that it simplifies the rational 2/10 to 1/5 as the two rational fraction are equivalent. This is illustrated by: In[15]:= 2/10 === 1/5 Out[15]= True In[16]:= 2/10 //FullForm Out[16]//FullForm= Rational[1,5] Now it's reasonable that someone may want a set of rationals with a common denominator (perhaps because it is easier to look at, perhaps other reasons), but it would seem that this operation is appropriate most of the time and the burden of extra effort in the other cases is acceptable. Paul -----Original Message----- From: leigh pascoe [mailto:leigh at cephb.fr] To: mathgroup at smc.vnet.net Subject: [mg68695] [mg68677] Re: [mg68655] Re: MemberQ Peter Pein wrote: > leigh pascoe schrieb: > ... > >> While we are talking about MemberQ, what about the following behavior? >> In[15]:=Range[0,1,1/10] >> MemberQ[Range[0,1,1/10],2/10] >> >> Out[15]=\!\({0, 1\/10, 1\/5, 3\/10, 2\/5, 1\/2, 3\/5, 7\/10, 4\/5, >> 9\/10, 1}\) >> >> Out[16]=True >> >> Is the above result correct given that 2/10 doesn't appear in the >> list produced by the range statement?? >> > > Mathematica automagically cancels 2/10. > > >> On the other hand 0.5 can be >> represented exactly as a binary number, but >> In[29]:=MemberQ[Range[0,1,1/10],.5] >> >> Out[29]=False >> >> > > 1/2 has head Rational, 0.5 has got head _Real. So they must not be the same. > > >> LP >> >> > > I wrote a (very) small package: > > http://people.freenet.de/Peter_Berlin/Mathe/NMemberQ/NMemberQ.m > and > http://people.freenet.de/Peter_Berlin/Mathe/NMemberQ/NMemberQ.nb > > Feel free to add the function NMemberQ to your own collection of utilities. > > Cheers, > Peter > > > > Dear Peter, Thanks for your reply. Bruce Colletti was the original poster of this topic and will probably be interested in your function NMemberQ[]. As others have pointed out the use of MemberQ to compare fixed precision (Real) and Rational numbers produces unpredictable (machine and version dependent) results. My main point was that any such comparison should produce an error or warning that the comparison is not reliable, rather than True or False. It still strikes me as strange that In[8]:=.7//FullForm Range[0.,1.,.1][[8]]//FullForm MemberQ[Range[0.,1.,.1],.7] Out[8]//FullForm=0.7` Out[9]//FullForm=0.7000000000000001` Out[10]=True returns True for two numbers that Ma tells me are different. Leigh