Code Producing Power::Infty

Question

I tried computing the following

Unprotect[C]
\[Psi] = Sqrt[2] - 1;
\[Epsilon] = .001;
\[Omega] = 50000;
k = 13;
j = 3;
    A1 = Flatten[
    Table[(s1^j)/(s2^k), {s2, 1, Floor[\[Omega]^(1/k)]}, {s1,Ceiling[((s2^k) (\[Psi] - \[Epsilon]))^(1/j)], 
    Floor[((s2^k) (\[Psi] + \[Epsilon]))^(1/j)] }]];
  A2 = Flatten[
    Table[(s1^j)/(s2^k), {s1, 1, Floor[\[Omega]^(1/j)]}, {s2, 
      Ceiling[((s1^j)/(\[Psi] + \[Epsilon]))^(1/k)], 
      Floor[((s1^j)/(\[Psi] - \[Epsilon]))^(1/k)]}]];
  A = DeleteDuplicates[Flatten[Intersection[A1, A2]]];
  C1 = DeleteDuplicates[
    Flatten[Table[(s1^j)/(2 s2 + 1)^k, {s2, 1, 
       Floor[(10 \[Omega])^(1/k)]}, {s1, 
       Ceiling[(((2 s2 + 1)^k) (\[Psi] - \[Epsilon]))^(1/j)], 
       Floor[(((2 s2 + 1)^k) (\[Psi] + \[Epsilon]))^(1/j)]}]]];
  C2 = DeleteDuplicates[
    Flatten[Table[(s1^j)/(2 s2 + 1)^k, {s1, 1, 
       Floor[(10 \[Omega])^(1/j)]}, {s2, 
       Ceiling[(((s1^j)/(\[Psi] + \[Epsilon]))^(1/k) - 1)/2], 
       Floor[(((s1^j)/(\[Psi] - \[Epsilon]))^(1/k) - 1)/2]}]]];
  C = DeleteDuplicates[Flatten[Intersection[C1, C2]]];
  g1 = N[Length[Intersection[A, C]]/Length[A]];

When j=1 the code works fine but when j is an integer greater than 1, it returns an error sign:

Power::infy: Infinite expression 1/0 encountered.

Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered.

I tried fixing it using DeleteCases to delete the zeros (see t1 and t2)

Unprotect[C]
    \[Psi] = Sqrt[2] - 1;
    \[Epsilon] = .001;
    \[Omega] = 50000;
    k = 13;
    j = 3;
t1 = DeleteCases[
  Table[s1, {s1, Ceiling[((s2^k) (\[Psi] - \[Epsilon]))^(1/j)], 
    Floor[((s2^k) (\[Psi] + \[Epsilon]))^(1/j)]}], 0]
t2 = DeleteCases[
  Table[s2, {s2, Ceiling[((s1^j)/(\[Psi] + \[Epsilon]))^(1/k)], 
    Floor[((s1^j)/(\[Psi] - \[Epsilon]))^(1/k)]}], 0]
        A1 = Flatten[
        Table[(s1^j)/(s2^k), {s2, 1, Floor[\[Omega]^(1/k)]}, {s1,t1 }]];
      A2 = Flatten[
        Table[(s1^j)/(s2^k), {s1, 1, Floor[\[Omega]^(1/j)]}, {s2, 
         t2}]];
      A = DeleteDuplicates[Flatten[Intersection[A1, A2]]];
      C1 = DeleteDuplicates[
        Flatten[Table[(s1^j)/(2 s2 + 1)^k, {s2, 1, 
           Floor[(10 \[Omega])^(1/k)]}, {s1, 
           Ceiling[(((2 s2 + 1)^k) (\[Psi] - \[Epsilon]))^(1/j)], 
           Floor[(((2 s2 + 1)^k) (\[Psi] + \[Epsilon]))^(1/j)]}]]];
      C2 = DeleteDuplicates[
        Flatten[Table[(s1^j)/(2 s2 + 1)^k, {s1, 1, 
           Floor[(10 \[Omega])^(1/j)]}, {s2, 
           Ceiling[(((s1^j)/(\[Psi] + \[Epsilon]))^(1/k) - 1)/2], 
           Floor[(((s1^j)/(\[Psi] - \[Epsilon]))^(1/k) - 1)/2]}]]];
      C = DeleteDuplicates[Flatten[Intersection[C1, C2]]];
      g1 = N[Length[Intersection[A, C]]/Length[A]];

However, I continue to get Power::Infty.

How do we fix my code?

Answer 1

Your code is working as intended. As others have mentioned in the comments, your code could use some cleaning up. But the basic issue is when $j>1$ both A1 and A2 are empty (the bounds on your table are trivial). That means Intersection[A1, A2] is empty so A is empty and Length[A]==0. This gives g1 = N[Length[Intersection[A, C]]/Length[A]] $=$ Something$/0$ which gives your error. So the question is, what do you want g1 to be when Length[A]==0? Whatever you want to do, you can accomplish it simply by doing

g1 = If[Length[A]>0, N[Length[Intersection[A,C]]/Length[A]], 
   "Whatever you want. Some value, raise an error, abort, ...etc."];