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

I propose a strategy that uses RealDigits to compare the actual digits of the numbers. The only tricky bit is stripping out trailing zeroes.

trunc = {Drop[First@#, Plus @@ First /@ {-Dimensions@First@#, 
         Last@Position[First@#, n_?(# != 0 &)]}], Last@#} &@ RealDigits@# &;
exactEqual = SameQ @@ trunc /@ {#1, #2} &;

In[1]  := exactEqual[1.000000000000000000000000000000000000000000000000000111,
                     1.000000000000000000000000000000000000000000000000000111000]
Out[1] := True
In[2]  := exactEqual[1.000000000000000000000000000000000000000000000000000111,
                     1.000000000000000000000000000000000000000000000000000112000]
Out[2] := False