Is ad infinitum in actu Provable? (a critical study)

As a philosophical question covering issues such as whether dimensions of the world are finite or infinite, the possibility of indivisible part, the possibility of an infinite thing, whether time and temporal past incidents are finite or infinite, and regressio ad infinitum in the chain of causes and effects, "Ad infinitum in actu" has since long caught the attention and disputes of scholars. Some of them have argued for the possibility and some for the impossibility of it. There are others who considered the arguments of both sides inadequate and thus remained silent about the issue. Following Kantor's efforts, it was embraced that "Ad infinitum in actu" is neither provable nor refutable logically. Having embraced that mathematics of infinitum in actu cannot be proved nor can it be decided about and that it is far from mathematics of finitude, at last ad infinitum in actu was accepted as one postulate in the theory of postulates of sets.    In their essay showing that ad infinitum in actu is far from mathematical infinitum, the authors have suggested an argument to demonstrate that infinitum in actu is mathematically unprovable. It will become evident that mathematical arguments for the refutation of ad infinitum in actu (such as those of comparison, of the side and the middle, of ladder, and so on) are not real arguments, rather they are mere hints to more illuminate the consequences of the concept of ad infinitum in actu in the light of which one can decide about the possibility or impossibility of ad infinitum in actu.