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Series and Sqrt problem (a bug?)

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  • Subject: [mg86926] Series and Sqrt problem (a bug?)
  • From: GS <vokaputs at>
  • Date: Wed, 26 Mar 2008 04:54:56 -0500 (EST)

Numerically Mathematica defines square root of a positive number as a
positive number:
In[1]:= Sqrt[2.]
Out[1]= 1.41421

It is careful enough not to simplify a square root of a square:
In[2]:= Sqrt[x^2]
Out[2]= Sqrt[x^2]
because x can be either positive or negative.

However, when I specify that x approaches minus infinity, and use
Series, it assumes that Sqrt[x^2] is equal to x:
In[4]:= Series[Sqrt[x^2], {x, -Infinity, 1}] // Normal
Out[4]= x

It does the same thing when x approached plus infinity:
In[5]:= Series[Sqrt[x^2], {x, Infinity, 1}] // Normal
Out[5]= x

This does not seem right to me, and caused grievances in my recent
research problem.

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