This is the Epsilon Delta Definition of Continuity | Real Analysis скачать в хорошем качестве

This is the Epsilon Delta Definition of Continuity | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier!    / @wrathofmath   🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course:    • Real Analysis   Real Analysis exercises:    • Real Analysis Exercises   Get the textbook! https://amzn.to/45kcMjq The epsilon delta definition of continuity is the end of our quest for a rigorous definition of continuity. All quirks of continuity we have seen are consistent with this definition which mostly comes from the definition of a functional limit. A function f is continuous at a point c if for all epsilon greater than 0, there exists delta greater than 0 so |x-c| less than delta implies |f(x)-f(c)| less than epsilon. In this real analysis lecture we introduce this definition, equivalent definitions, properties of continuity, and a basic epsilon delta proof. #realanalysis Definition of a Functional Limit:    • Epsilon-Delta Definition of Functional Lim...   Proof sqrt(x) is Continuous:    • Proof: sqrt(x) is Continuous using Epsilon...   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath 0:00 Intro 1:01 Definition 3:25 Why |x-c| isn't Required to be Positive 4:12 When c is not a Limit Point 5:37 Equivalent Definitions of Continuity 7:07 Sequential Characterization of Continuity 8:19 Proving f(x)=x is Continuous using Epsilon Delta Definition of Continuity 9:56 Basic Continuity Laws 11:13 Practice Exercise: Prove sqrt(x) is Continuous