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Epsilon-Delta Definition of Functional Limits | Real Analysis

We introduce the epsilon delta definition of the limit of a function. We will explain the definition of a functional limit in depth, see some visualizations of it, discuss the negation of the definition of a limit, and then complete two epsilon-delta limit proofs for practice. #realanalysis 0:00 - Intro 0:59 - Epsilon Delta Definition of Limit of a Function 7:22 - Negation of the Definition (Function not Having a Particular Limit) 9:25 - Epsilon Delta Limit Proof 1 13:40 - Epsilon Delta Limit Proof 2 19:28 - Recap 20:05 - Epsilon Delta Limit Problem 20:54 - Outro Oh My God Continuity is Weird: (coming soon) Limit of a Function is Unique:    • Proof: Limit of a Function is Unique ...   Connecting Function Limits and Sequence Limits:    • Connecting Function Limits and Sequen...   Show Function Limit Doesn't Exist:    • Show Function Limit Doesn't Exist wit...   Properties of Functional Limits:    • Proving all the Function Limit Laws |...   Definition of Continuity:    • This is the Epsilon Delta Definition ...   Real Analysis Course:    • Real Analysis   Real Analysis exercises:    • Real Analysis Exercises   ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★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 Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020