On 13 November 2010 04:36, Robert Bradshaw <rober...@math.washington.edu> wrote:
> On Fri, Nov 12, 2010 at 3:44 PM, Derrick <we.sana...@gmail.com> wrote:
>> Any clue why bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2)))) returns
>> false where the expressions are mathematically equivalent.
>
> Because an expression being equal to zero is, in general, and
> undecideable question. If it can't tell, it'd rather error on the side
> of caution (not being equal) than claim they're equal.
It's not clear to me why claiming two things are false when they are
true, is any better/worst they are true when in fact they are false.
They are both 100% wrong.
Surely the better approach is to return 'Unknown' or something else to
indicate something is unknown, rather than claim its false when its
true.
Here's the same sort of thing in Mathematica.
In[3]:= 12 == 2
Out[3]= False
In[4]:= 1 == 1
Out[4]= True
In[5]:= AcrSin[x] == 2 ArcTan[x/(1+Sqrt[1+x^2])]
x
Out[5]= AcrSin[x] == 2 ArcTan[----------------]
2
1 + Sqrt[1 + x ]
In[7]:= x^3 == x x^2
Out[7]= True
As you can see, when Mathematica does not know if the expression is
true or false, it returns the expression, not "True" or "False".
Dave
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