Explore the intricacies of infinite sequences and rational polynumbers in this 48-minute mathematics lecture. Delve into the concept of on-sequences generated by rational functions, examining their delicate nature through factorizations. Discover the introduction of a new symbol for "infinity" and its relationship to limiting behavior. Learn about arithmetic with rational polynumbers, their distinction from functions, and the illegality of division by zero. Investigate the evaluation and equality of rational polynumbers, and visualize concepts through graphical representations. Gain valuable insights into this advanced mathematical topic, building a strong foundation for further study in real numbers and limits.