Re: Why does Reduce work this way ...?

• To: mathgroup at smc.vnet.net
• Subject: [mg67251] Re: Why does Reduce work this way ...?
• Date: Wed, 14 Jun 2006 06:29:14 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 6/13/06 at 1:07 AM, jackgoldberg at comcast.net wrote:

>This post is related to a previous series of posts about ReplaceAll
>in a set of inequalities. I have "reduced" the problem to this
>unexpected situation:

>In[1]  FullForm[-3<=x<=1]
>Out[1]  LessEqual[-3,x,1]

>In[2] Reduce[-3<=x<=1] Out[2]  -3<=x<=1

>In[3]  FullForm[%2]
>Out[3]  Inequality[-3, LessEqual, y, LessEqual,1]

>In[4] Reduce[ LessEqual[-3,x,1]
>Out[4] -3 &#8804; x &#8804; 1

>In[5] FullForm[%4]
>Out[5]  Inequality[-3, LessEqual, y, LessEqual,1]

>This defies my understanding.  What is qoing on with Reduce?

Hmm... You didn't say what version of Mathematica you are using. With

In[13]:=
\$Version

Out[13]=
5.2 for Mac OS X (June 20, 2005)

I get

In[14]:=
Reduce[LessEqual[-3,x,1]]

Out[14]=
-3 <= x <= 1

and since

In[15]:=
Inequality[-3,LessEqual,x,LessEqual,1]

Out[15]=
-3 <= x <= 1

I am not seeing any inconsistency
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```

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