       Re: Using Equal with Real Numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg123180] Re: Using Equal with Real Numbers
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 25 Nov 2011 04:57:45 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111241153.GAA28857@smc.vnet.net>

```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:= list1 = Range[0, 1, 0.1]
> Out= {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:= list1 // InputForm
>
> Out//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:= {MemberQ[list1, 0.6], MemberQ[list1, 0.7]}
> Out= {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:= list2 = range[0, 1, 0.1]
> Out= {0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.}
>
> In:= list2 // InputForm
> Out//InputForm= {0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,
> 1.}
>
> In:= {MemberQ[list2, 0.6], MemberQ[list2, 0.7]}
> Out= {True, True}
>
>
>

```

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