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Explore a thought-provoking lecture on the Continuum Hypothesis and its generalization in set theory. Delve into the philosophical implications and contemporary perspectives surrounding these fundamental mathematical concepts. Examine the historical context of Cantor's postulation and the subsequent developments in set theory. Investigate the notion of independence in mathematical axioms and its impact on our understanding of infinite sets. Consider the philosophical acceptability of various approaches to resolving or accepting the non-resolution of these hypotheses. Reflect on the intriguing question of whether Cantor himself would comprehend modern solutions to his own inquiry. Gain insights into the ongoing discourse within the mathematical community regarding these foundational questions in set theory.