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MathGroup Archive 2011

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Re: Bug 1+4/10

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120036] Re: Bug 1+4/10
  • From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
  • Date: Thu, 7 Jul 2011 07:27:09 -0400 (EDT)
  • References: <iv1acv$sk7$1@smc.vnet.net>

On Wed, 06 Jul 2011 10:37:35 +0100, slawek <slawek at host.pl> wrote:

> Let check
>
> In[1]:= 1.4 == 1 + 4/10
> Out[1]= True
>
> In[2]:= a = SetPrecision[1.4, 30]
> Out[2]= 1.39999999999999991118215802999
>
> In[3]:= b = SetPrecision[1 + 4/10, 30]
> Out[3]= 1.40000000000000000000000000000
>
> No comment is needed.
>
> slawek

Yet:

In[4] :=
a == b

Out[4] =
False

So here we have shown that a number padded with binary zeros is generally  
not equal to the same number padded with decimal zeros. I doubt anyone can  
be surprised by this. However, they are still comparable in a sense:

In[5] :=
a = SetPrecision[Interval[1.4], 30]

Out[5] =
Interval[{1.39999999999999968913755310495,
           1.40000000000000013322676295502}]

In[6] :=
b = SetPrecision[Interval[1 + 4/10], 30]

Out[6]=
Interval[{1.40000000000000000000000000000,
           1.40000000000000000000000000000}]

In[7] :=
IntervalMemberQ[a, b]

Out[7] =
True

Proper treatment of inexact numbers requires at least some care and  
attention. It is important to remember that one is operating on  
distributions rather than points, so simplistic notions of arithmetic  
equality are not meaningful.


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