Re: Using Equal with Real Numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg123160] Re: Using Equal with Real Numbers
• From: Gabriel Landi <gtlandi at gmail.com>
• Date: Fri, 25 Nov 2011 04:54:08 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111241153.GAA28857@smc.vnet.net> <6A41692C-6AC4-4F55-9A6A-E292D36265DA@mimuw.edu.pl>

```Dear Andrzej,

Indeed, your solution solves the problem of MemberQ.
However, there are other situations where I have encountered similar
problems. Here is an example:

list=Range[0,1,0.1];

Do[ f[x] = x^2, {x,list}]

Now, even though f[0.6]=0.36, f[0.7] is undefined, for the very same
reason.

Best regards,

Gabriel Landi

On Nov 24, 2011, at 10:42 AM, Andrzej Kozlowski wrote:

> MemberQ does not test for mathematical equality but only for matching
(as pattern). It's easy to write a function that will test whether
something is Equal (in Mathematica's sense, of course)   to an element
of a list e.g.:
>
> memberQ[l_List, a_] := Or @@ Thread[l == a]
>
>
> list1 = Range[0, 1, 0.1];
>
> {memberQ[list1, 0.6], memberQ[list1, 0.7]}
>
> {True,True}
>
> Andrzej Kozlowski
>
>
>
> On 24 Nov 2011, at 12:53, Gabriel Landi wrote:
>
>> Dear MathGroup members,
>>
>> Using statements like x1=x2, with real numbers is problematic in
>> most programming languages.
>> Below I briefly discuss an example with Mathematica and then show the
>> rather truculent solution that I've come up with.
>> I would love to hear your comments on this and perhaps other (likely
>> better) solutions.
>>
>> Best Regards,
>>
>> Gabriel Landi
>>
>>
>>
--------------------------------------------------------------------------

>>
--------------------------------------------------------------------------

>>
--------------------------------------------------------------------------

>> ---
>>
>> Consider:
>>
>> In[187]:= list1 = Range[0, 1, 0.1]
>> Out[187]= {0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.}
>>
>> Using InputForm we see that:
>>
>> In[188]:= list1 // InputForm
>>
>> Out[188]//InputForm={0., 0.1, 0.2, 0.30000000000000004, 0.4, 0.5,
>> 0.6000000000000001, 0.7000000000000001,
>> 0.8, 0.9, 1.}
>>
>> That is, 0.3, 0.6 and 0.7 have some round-off error.
>>
>> Now:
>>
>> In[200]:= {MemberQ[list1, 0.6], MemberQ[list1, 0.7]}
>> Out[200]= {True, False}
>>
>> (This actually depends on the OS and perhaps other things). The point is
>> that he recognizes 0.6 as a member of list1 but not 0.7, even though
>> both have the same InputForms.
>> This issue, as you may imagine, prohibits one from using functions that
>> implicitly make use of =, when dealing with real numbers.
>>
>> Here is my solution:
>>
>> range[xi_, xf_, df_] := N@Rationalize@Range[xi, xf, df]
>>
>> That is, I redefine the range function. It first rationalizes the
>> entries and then transform them into numeric quantities. Not only is
>> this crude, but is likely quite slow for long lists. Notwithstanding, it
>> does solve the problem in the previous example:
>>
>> In[190]:= list2 = range[0, 1, 0.1]
>> Out[190]= {0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.}
>>
>> In[191]:= list2 // InputForm
>> Out[191]//InputForm= {0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,
>> 1.}
>>
>> In[201]:= {MemberQ[list2, 0.6], MemberQ[list2, 0.7]}
>> Out[201]= {True, True}
>>
>>
>>
>

```

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