This is what my city's site said:
No more than 3 pet animals are permitted on a single premise within the city. Animals include dogs, cats, rabbits, or other animals, excluding tropical fish or exotic fish, but including birds maintained outside the living area of the residential structure. No keeping of poultry, domestic fowl, pigs, hogs, or livestock shall be permitted within the city limits.

I however live well outside the city and there are no limitations as to how many pets are keep here.