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Re: Re: MemberQ

• To: mathgroup at smc.vnet.net
• Subject: [mg68612] Re: [mg68561] Re: MemberQ
• From: leigh pascoe <leigh at cephb.fr>
• Date: Sun, 13 Aug 2006 05:52:21 -0400 (EDT)
• References: <0533005404FE2E45B90AF737DE5A991A015312F3@de01exm67.ds.mot.com>
• Sender: owner-wri-mathgroup at wolfram.com

Erickson Paul-CPTP18 wrote:
> Only curious if for you 
> .7//FullForm
> doesn't return 0.7000000000000001`
>
> -----Original Message-----
> From: leigh pascoe [mailto:leigh at cephb.fr] 
To: mathgroup at smc.vnet.net
> Subject: [mg68612] [mg68561] Re: MemberQ
>
> Adriano Pascoletti wrote:
>   
>> Bruce Colletti wrote ..
>>   
>>     
>>> Re Mathematica 5.2.0.0.
>>>
>>> Since 0.7 is in the set {0.0, 0.1, 0.2,..., 0.9, 1.0}, why does 
>>> MemberQ[Range[0., 1., .1], .7] return False?
>>>  
>>> Thankx.
>>>
>>> Bruce
>>>
>>>     
>>>       
>> Because the 0.7 in Range[0.0, 1.0, 0.1] is
>>
>> In[11]:=
>> Range[0.0,1.0,0.1][[8]]//FullForm
>> Out[11]//FullForm=
>> 0.7000000000000001`
>>
>> and
>>
>> In[9]:=
>> FullForm[0.7]
>> Out[9]//FullForm=
>> 0.7`
>>
>> They differ on the 16th decimal place as can be seen  evaluating
>> 0.7 - Range[0.0, 1.0, 0.1]
>>
>>
>>
>> Adriano Pascoletti
>>
>>
>>
>>   
>>     
> So the curious thing is that it returns True for Ssezi and for me!
>
> In[8]:=Range[0.,1.,.1][[8]]//FullForm
> MemberQ[Range[0.,1.,.1],.7]
>
> Out[8]//FullForm=0.7000000000000001`
>
> Out[9]=True
>
> LP
>
>
>
>
>   
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

It seems to me that a better behavior would be an error message: "Exact 
numbers and fixed precision numbers cannot be compared with MemberQ" or 
perhaps just "False".

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?? 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

LP