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 think that you really have to specify what you want... there's no way to compare approximate real numbers that will satisfy everyone in every situation.

Anyway, here's a couple more options:

In[1]:= realEqual[lhs_,rhs_,tol_:$MachineEpsilon] := 0==Chop[lhs-rhs,tol]

In[2]:= Equal[1.0000000000000021,1.0000000000000021]
        realEqual[1.0000000000000021,1.0000000000000021]
Out[2]= True
Out[3]= True

In[4]:= Equal[1.0000000000000022,1.0000000000000021]
        realEqual[1.0000000000000022,1.0000000000000021]
Out[4]= True
Out[5]= False

As the precision of both numbers gets higher, then they can always be distinguished if you set tol high enough.

Note that the subtraction is done at the precision of the lowest of the two numbers. You could make it happen at the precision of the higher number (which seems a bit pointless) by doing something like

maxEqual[lhs_, rhs_] := With[{prec = Max[Precision /@ {lhs, rhs}]}, 
  0 === Chop[SetPrecision[lhs, prec] - SetPrecision[rhs, prec], 10^-prec]]

maybe using the minimum precision makes more sense

minEqual[lhs_, rhs_] := With[{prec = Min[Precision /@ {lhs, rhs}]}, 
  0 === Chop[SetPrecision[lhs, prec] - SetPrecision[rhs, prec], 10^-prec]]