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Explore the intricacies of number systems in this 49-minute lecture by Kevin Hare from the University of Waterloo, presented as part of the Spec(Q¯(2πi)) conference at the Fields Institute. Delve into the fundamental concepts and advanced theories surrounding various number systems, gaining insights into their properties, applications, and significance in mathematics. Enhance your understanding of numerical representations and their role in mathematical analysis and problem-solving.