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'm not aware of an already defined operator. But you may define for example:

longEqual[x_, y_] := Block[{$MaxPrecision = 20, $MinPrecision = 20},
                            Equal[x - y, 0.]]  

Such as:

longEqual[1.00000000000000223, 1.00000000000000223]
True
longEqual[1.00000000000000223, 1.00000000000000222]
False   

Edit

If you want to generalize for an arbitrary number of digits, you can do for example:

longEqual[x_, y_] :=
 Block[{
   $MaxPrecision =  Max @@ StringLength /@ ToString /@ {x, y},
   $MinPrecision =  Max @@ StringLength /@ ToString /@ {x, y}},
   Equal[x - y, 0.]]

So that your counterexample in your comment also works.

HTH!