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Greater implies unequal?


Hello:
I'm using Mathematica v5. Why do I get?:

Clear[a]; Remove[a]
In[43]:=
Simplify[Sqrt[a]!=0,a>0]

Out[43]=
Sqrt[a] != 0

In[46]:=
Simplify[Sqrt[2]!=0,a>0]

Out[46]=
True

In[47]:=
2!=3

Out[47]=
True

In[48]:=
Simplify[Sqrt[2 a]!=0,a>0]

Out[48]=
Sqrt[a] != 0


Does anyone else get this? The main problem is In[43] and Out[43]. I checked
that "a" does not have a pre-defined value, or Sqrt. I also get :

In[50]:=
Simplify[Sqrt[a]>0,a>0 ]

Out[50]=
True
  In[51]:=
Simplify[Sqrt[a]<0,a>0 ]

Out[51]=
False
Well, I think it makes more sense that Out[50]or Out[51] were undefined...



Atte. Andres Guzman



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