Скачать или смотреть Composition of Continuous Functions is Continuous | 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

We prove the composition of continuous functions is continuous using the sequence definition of continuity. We assume g is a function from A to B, and f is a function from B to the reals. We assume g is continuous at c in A and f is continuous at g(c) in B. We can then apply the sequential definition of continuity to prove that any sequence in A converging to c has a sequence of images converging to f(g(c)). #realanalysis

Definition of Continuity:    • This is the Epsilon Delta Definition of Co...  
Basic Continuity Laws:    • Proving the Algebraic Continuity Laws | Re...  
Sequential Characterization of Continuity:    • Definition of Continuity with Sequences! |...  

★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

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu