Mathematics for Data Science 1 - W1_L3: Real & complex numbers - understanding rational & irrational numbers

Welcome to Week 1 Lecture 3 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture explores the limitations of rational numbers and introduces the concept of irrational and real numbers. We begin with a review of natural numbers, integers, and rational numbers before explaining why rational numbers, though dense, don’t cover the full number line. The session highlights irrational numbers such as √2 and π, which cannot be expressed in the form p/q. Finally, we define the real numbers as the union of rational and irrational numbers, emphasizing their density, and provide a brief introduction to complex numbers and their role in extending number systems. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, Visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #Mathematics #DataScience #MathForDataScience #RealNumbers #RationalNumbers #IrrationalNumbers #NumberSystems #Integers #NaturalNumbers #Density #SquareRoot #Pi #NumberLine #Lecture #Education #ComplexNumbers #Pythagoras #e #PerfectSquares #IITMadrasBS #OnlineLearning #MathBasics