Each Series was created with the class constructor which accepts a wide variety of inputs with the simplest being a sequence of values for each of the parameters index and data.

Mathematical Cartesian products are slightly different from the outcome of operating on two pandas objects. Each a label in s1 pairs up with each a label in s2. This pairing produces six a labels, three b labels, and one c label in the resulting Series. A Cartesian product happens between all identical index labels.

As the element with label c is unique to Series s2, pandas defaults its value to missing, as there is no label for it to align to in s1. Pandas defaults to a missing value whenever an index label is unique to one object. This has the unfortunate consequence of changing the data type of the Series to a float, whereas each Series had only integers as values. This occurred because of NumPy's missing value object; np.nan only exists for floats but not for integers. Series and DataFrame columns must have homogeneous numeric data types; therefore, each value was converted to a float. This makes very little difference for this small dataset, but for larger datasets, this can have a significant memory impact.