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Explore the fascinating world of successor-limit hierarchy and self-similarity in this 42-minute mathematics lecture. Delve into the intricate levels of limits in the sequence, pushing mathematical boundaries to extraordinary heights. Examine the computational challenges that arise, offering programmers unique opportunities to contribute to pure mathematics. Learn about the self-similar properties reminiscent of fractals and discuss the philosophical implications of these extreme numerical constructs. Gain insights into the intersection of computer science and advanced mathematics while considering the practical applications and theoretical significance of these complex mathematical structures.