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Section 0.5 Basic Set Theory

Figure 0.5.1. Cantor Middle Third Set

“The creation of set theory is generally credited to the German mathematician Georg Cantor, in the late nineteenth century. Previously, sets had seldom been regarded as entities worthy of study in their own right; but Cantor, originally motivated by a problem in Fourier analysis, developed an extensive theory. Among many other things, he showed that there are different sizes of infinity, proving, for instance, that there is no bijection between \(\mathbb{R}\) and \(\mathbb{N}\text{.}\)” [Leinster, 2016. Basic Category Theory.]