Hello,
If I try to simplify Sqrt[x^2] - Abs under the assumptions x>0 and x<=0 separately, it works correctly, but if I combine them into one condition it does not:
Simplify[Sqrt[x^2] - Abs[x],x<=0]
0
Simplify[Sqrt[x^2] - Abs[x],x>0]
0
Simplify[Sqrt[x^2] - Abs[x],(x>0) || (x<=0)]
Sqrt[x^2] - Abs[x]
Why did it leave the expression unevaluated for (x>0) || (x<=0) case? It should evaluate to 0 like in the other two cases. What am I missing? Thank you.
Curiously, if I use Element[x,Reals] as a condition then it works:
Simplify[Sqrt[x^2]-Abs[x],Element[x,Reals]]
0
So, apparently, Element[x,Reals] and (x>0) || (x<=0) is not the same thing, oddly enough...