I am using inequalities to follow some line of reasoning in Mathematica and I came across a problem I can not explain to myself. Does from a>=0 and b>=0 not follow a+b >= 0? How does Mathematica evaluate these statements? Thanks!
In[225]:= Refine[(A0 c0 (c - c1) >= 0),
A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]
Out[225]= True
In[226]:= Refine[(A (c0 - c1) c1 >= 0),
A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]
Out[226]= True
In[227]:= Refine[(A0 c0 (c - c1) + A (c0 - c1) c1 >= 0),
A0 >= 0 && A >= A0 && A1 >= A && c1 >= 0 && c > c1 && c0 >= c]
Out[227]= A0 c0 (c - c1) + A (c0 - c1) c1 >= 0
Refine[a + b >= 0, a >= 0 && b >= 0]returnsTrue, so it is likely the complexity of the final statement that is giving Mathematica trouble. – rcollyer Jan 15 at 15:58