The scope of this video lesson consists in studying the sets of Rational and Irrational numbers. The main objectives for the students are: 1) Learning how to distinguish between a rational number and an irrational number; 2) Learning about the existence of 2 infinities: the “countable infinity” for sets of Rational numbers and the “uncountable infinity” for the set of irrational numbers; and 3) Learning to use straightforward and advanced tools from Mathematics to reach goals (1) and (2). Such tools include: Methods of proofs, Euclidean Division and the Pigeonhole Principle, at the basic level, in adition to Cantor’s proof of uncountability at an upper level. The students should be aware of some definitions in Discrete Mathematics such as: sets, unions, intersections; logical definitions of “implies that” (“if then”) and equivalences (“if and only if”); some knowledge of elementary probability definition; and one-to-one mappings (bijection). This video lesson spans about 32 minutes and provides 7 exercises for students to work out in groups and in consultation with their classroom teacher. The exercises exclude the main question of the lesson, which should trigger the students’ interest in the lesson. The entire duration of the video demonstration and exercises should take about 50 minutes or equivalently one classroom session. To complete the lesson, a calculator is needed. The calculator’s functionalities should include the square root function and the number Pi. (Note that, nowadays, smartphone calculators include those functionalities.)