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As it is well known, mathematics became a deductive science in ancient Greece. Already in 6th century BC, Greek philosophers studied the problem of infinity and the continuous and discrete problems related to it. Aristotle paid much attention to the development of this concept. He was the first who categorically began to object against the application of the actual infinity in science, referring to the fact that, despite knowing the methods of counting the finite number of objects, we cannot use the same methods to infinite sets. In his Physics, Aristotle stated as follows:

“There remains the alternative, according to which the infinite has only potential existence . .. The actual infinite is not exist.”

According to Aristotle, mathematics does not need actual infinity. Aristotle is the author of the famous thesis Infinitum Actu Non Datur, which translates from Latin as the statement about the impossibility of the existence of the logical or mathematical (that is, only imaginable, but not existing in Nature) actual-infinite objects.