Is there a “normal” EqualQ function in Mathematica?

Question

On the documentation page for Equal we read that

Approximate numbers with machine precision or higher are considered equal if they d

Answer 1

Try this:

realEqual[a_, b_] := SameQ @@ RealDigits[{a, b}, 2, Automatic]

The choice of base 2 is crucial to ensure that you are comparing the internal representations.

In[54]:= realEqual[1.0000000000000021, 1.0000000000000021]
Out[54]= True

In[55]:= realEqual[1.0000000000000021, 1.0000000000000022]
Out[55]= False

In[56]:= realEqual[
           1.000000000000000000000000000000000000000000000000000000000000000022
         , 1.000000000000000000000000000000000000000000000000000000000000000023
         ]
Out[56]= False