
Since this attitude persisted until almost the end of the 19th century, Cantor’s work was the subject of much criticism to the effect that it dealt with fictions-indeed, that it encroached on the domain of philosophers and violated the principles of religion. Since antiquity, a majority of mathematicians had carefully avoided the introduction into their arguments of the actual infinite (i.e., of sets containing an infinity of objects conceived as existing simultaneously, at least in thought). The theory had the revolutionary aspect of treating infinite sets as mathematical objects that are on an equal footing with those that can be constructed in a finite number of steps. The objects are called elements or members of the set. A set, wrote Cantor, is a collection of definite, distinguishable objects of perception or thought conceived as a whole. This theory grew out of his investigations of some concrete problems regarding certain types of infinite sets of real numbers. The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts.īetween the years 18, the German mathematician and logician Georg Cantor created a theory of abstract sets of entities and made it into a mathematical discipline. Set theory, branch of mathematics that deals with the properties of well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions.
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