For an infinitely long wing, there would be no induced drag at any angle of attack.
Induced drag is the result of the the modification of the local airflow direction by the vortices that result from having a finite span. The vortices tilt the air as it approaches the wing by adding a downwash. It is this difference between the freestream and the local airflow direction that manifests itself as induced drag.
So, suppose that you are changing the angle of attack of an infinite, symmetrical airfoil.
Due to symmetry of the airfoil relative the the plane along the airfoil, the lift is zero at zero angle of attack. Drag is nonzero.
At AoA-s which are small and negative, or else close to 360 degrees, the lift shall be downwards.
Now, when the AoA is 180 degrees, lift is zero for the same symmetry reasons.
If the airfoil´s leading and trailing edge are not symmetrical, the lift would not be zero at exactly 90 degrees, but it would go through zero at near 90 degrees.
However, at small positive AoA-s, lift and drag both increase with AoA.
Is the increase of drag compared to zero-lift drag called "induced drag" in case of an infinite airfoil?