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C HAPTER 3. C ANTOR ’ S U NDERSTANDING OF AN I NFINITE .
Georg Cantor was one of the most prominent mathematicians of the nineteenth century.
Cantor was born in St. Petersburg in 1845 and died in Halle in 1918. He was educated in
Germany and received his doctorate from the University of Berlin in 1868, which was the
leading center of mathematical research in Europe. Cantor studied under and worked with the
most famous mathematicians of his time: Kummer, Weierstrass, and Kronecker. Cantor’s
research in the theory of trigonometric series required him to provide a rigorous analysis of real
numbers. 105 In the process, Cantor gave mathematical content to the concept of an actual infinity
and showed that the notion of infinity was not meaningless. Infinity was not undifferentiated
because infinite sets could be rigorously compared and not all infinite sets were the same size.
Cantor believed that the transfinite numbers (infinite numbers which designate the various sizes
of infinite sets) were necessary for further development of mathematics. Because of this
conviction and because of a strong initial opposition among some mathematicians to the theory
of transfinite numbers, Cantor used not only mathematical but also philosophical and theological
105
Joseph W. Dauben,"Georg Cantor and the Battle for Transfinite Set Theory." Association of Christians in the
Mathematical Sciences. 2012, accessed June 12, 2018, https://acmsonline.org/home2/wp-
content/uploads/2016/05/Dauben-Cantor.pdf, 3.
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