According to Wikipedia, a reversible process is "a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, with no increase in entropy."
However, for isothermal processes, any reversible heat added to the system at constant temperature increases entropy. So, a reversible process of heating is causing a change in entropy. This seems to contradict the definition above.
Where have I gone wrong?