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Re: LessEqual vs Inequality, was ..Re: Replacement Rule with Sqrt in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg114720] Re: LessEqual vs Inequality, was ..Re: Replacement Rule with Sqrt in denominator
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 14 Dec 2010 06:54:59 -0500 (EST)
• References: <ie2971$mqh$1@smc.vnet.net> <4D050013.8050105@cs.berkeley.edu> <928BCB32-AEF9-4D13-87E0-BDDACF1BF878@mimuw.edu.pl> <4D055126.6080209@cs.berkeley.edu> <ie4mt7$9a7$1@smc.vnet.net> <4D0645BE.6000205@cs.berkeley.edu> <7F38BE28-6AE1-4BBC-A115-14B9CA3D9BF0@mimuw.edu.pl>

On 13 Dec 2010, at 17:53, Andrzej Kozlowski wrote:

>>
>> FullSimplify [Less[x,y,z]-Inequality[x,Less,y,Less,z] ]
>> does not reduce to zero, as it should.  So Mathematica, dare
>> I say, exhibits a bug.
>

In fact, I am (almost) amazed to see you claim that. There are certainly 
advantages to having a mathematics education for I am sure that nobody 
with that would ever expect this to work. What sort of algebraic 
structure is this subtraction taking place in, according to you? What 
sort of algebraic transformations is FullSimplify supposed to use here?


Good grief!

As I already pointed out:


Refine[Less[x, y, z], Inequality[x, Less, y, Less, z]] &&
 Refine[Inequality[x, Less, y, Less, z], Less[x, y, z]]

True

This simply means that truth of each expression implies the truth of the 
other - which is all that you could expect Mathematica to tell you.

And please do not point out that

(2 < 3) - (5 < 7)

 0

for you surely know that what is going on here has is an entirely 
different thing.

Andrzej Kozlowski