MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Archimedean Principle of Real Numbers | Real Analysis

Support the production of this course by joining Wrath of Math to access all my Real Analysis videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out my math fashion brand! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/4lNpyNN Business Inquiries: wrathofmathlessons@gmail.com Given real numbers a and b, where a is positive, we can always find a natural number m so that n*a is greater than b. In other words, we can add a to itself enough times to get a number greater than b. Equivalently, given any real number x, there exists a natural number greater than x, meaning the natural numbers are unbounded above. This is the Archimedean Principle, and we prove it in today's real analysis lesson. #realanalysis Definition of Supremum and Infimum: https://www.youtube.com/watch?v=QRGIhqz9vh4 Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu