The ionization energy is the energy required to remove an electron from an atom or molecule, specifically from its ground state. While it is true that, theoretically, an infinite amount of energy would be needed to completely remove an electron to an infinite distance from the nucleus, the concept of ionization energy typically refers to the energy required to remove an electron to a point where it is no longer bound to the atom or molecule.
In practice, when we talk about ionization energy, we are concerned with removing the electron from its bound state to a point where the attractive force of the nucleus is significantly weakened. This typically corresponds to moving the electron to a distance much larger than the size of the atom or molecule, but not necessarily to an infinite distance.
The ionization energy is a finite value because it represents the energy required to overcome the electrostatic attraction between the electron and the nucleus up to a certain point of separation. Once the electron is no longer bound to the atom or molecule, it can be considered ionized, even if it is not at an infinite distance.
It is important to note that the ionization energy can vary depending on the atom or molecule in question, as well as the specific energy level or orbital from which the electron is being removed. The ionization energy generally increases as you remove electrons from higher energy levels, closer to the nucleus, due to the increased electrostatic attraction between the remaining electrons and the positively charged nucleus.