Part 2/7:
Mathematics operates on defined rules and axioms. Axiomatically, if we have an infinite collection of non-empty sets, the Axiom of Choice posits that we can select one element from each set. While this might seem straightforward when applying to finite sets, challenges arise with infinite sets, particularly when no natural selection rule exists. Numerous arguments imply that such choices are not merely about picking the smallest number or adhering to definable patterns.
This brings us to the historical journey led by Georg Cantor in the late 19th century, whose pioneering work on infinity reshaped the mathematical landscape.