Fundamental Change in the Perception of Actual Infinity

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Fundamental Change in the Perception of Actual Infinity.
Introduction
In mathematics, the concept of cardinality has been in the minds of many people over time. Some don’t understand how the use of infinite numbers came into being. With this view, I have chosen to critically and prudently analyze set numbers, infinite numbers, and the history behind their existence. The paper will dive deeper into the evolution of infinity and the life of Georg Cantor to solve two key questions; What led to the revolutionary discovery of uncountable real numbers? What type of challenges were faced in developing infinite numbers? Therefore, my research paper aims to determine whether infinite numbers are and the main challenges faced by researchers in their research. This paper will be important because it will bring out the truth behind infinite numbers. My research has been based on research by a Russian mathematician, Georg Cantor, who is believed to be the father of actual infinity.
Historical Background.
It was believed that actual infinity was impossible by researchers like Aristotle in the 4th century B.C. In his recommendations, Aristotle believed that; if infinity were actual, something would have attained infinite magnitude and more significant than the heavens. He believed the study of infinity was too ambiguous and unattainable. Another researcher, Archimedes, in his research about numbers and infinity, started to believe infinite numbers existed and could be an infinite number more significant than the grains of sand in the entire universe (Bergbower). With these researchers not finding what infinity was, Georg Cantor emerged in 1874 and was interested in deriving a philosophical approach to analyzing infinite sets. Georg’s theory of actual infinite was opposed by many philosophes and theologians, Philosophers, and theologians, who considered infinity as the representation of God and eternity.
Georg made essential contributions in the study of set theory by proving its unique nature regarding finite exceptional sets (Manicosu). He developed "Transfinite Set Theory," a set theory that provides an insight into uncountable infinity. Many mathematicians and theologians viciously attacked Transfinite Set Theory and insulted Georg Cantor as a person. After getting humiliated by his mentor and peers, Cantor spent the rest of his life going deeper with his study of infinity. Eventually, Transfinite Set Theory was recognized by David Hilbert, and finally, the world starts to understand the value of his work (Rongrong). Through the work of these mathematicians, infinite numbers came into existence; it is important to note that more research needs to be done to further develop the concept of infinity.
Literature Review.
Georg Cantor developed set theory to study infinite numbers; it involves well-determined collections of objects represented in numbers. The theory employs a foundational system in the study of mathematics. The set theory is a pivotal contributor to discovering the currently used infinite numbers in the world. The set theory established that; it is possible to express items in a particular set of numbers. This knowledge set theory proved that even beyond a set of numbers, there is an infinite number that can represent objects in mathematics. This theory initially faced resistance from mathematicians of the day as they were not sufficiently convinced by the set theory (Liu et al.).
The theory e...