As you add or remove neutrons from the nucleus, isotopes are formed

That's true: isotopes are chemical elements with same atomic number (i. e. same number of protons) but different mass number (i. e. different number of protons+neutrons, so if the number of protons is the same, the number of neutrons should be different).

For instance, hydrogen has three different isotopes:

- protium, with only one proton in the nucleus

- deuterium, with one proton and one neutron

- tritium, with one proton and two neutrons