Power Sets and the Cardinality of the Continuum скачать в хорошем качестве

Power Sets and the Cardinality of the Continuum

Get better at math with Brilliant ► http://www.brilliant.org/treforbazett. Sign up for free, or the first 200 people who sign up using that link get 20% off an annual premium subscription. My thanks to Brilliant for sponsoring today's video! In this video we will learn about the power set, which is the set of all subsets of a given set. The cardinality of the power set of size n is given by 2^n. Finally, we will see a really interesting function that maps surjectively from the power set of the natural numbers using binary numbers to the interval [0,1] which is a continuum and we have previously seen by Cantor's diagonalization that [0,1] is uncountably infinite. In general, the power set of a set has a higher cardinality than the original set. 0:00 Definition of Power Sets 2:18 Example with 3 elements 3:10 Power Set of the Empty Set 4:33 Cardinality of a (finite) power set 5:52 Power Set of the Natural Numbers 10:22 Cardinality and uncountably infinite Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pag... COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography