Proof: Sequence Order Limit Theorem (Inequalities and Limits) | 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/3CMdgjI We prove the order limit theorem for convergent sequences. This proves that convergent sequences and their limits relate to each other and real numbers as we'd expect. For example if a_n converges to a and b_n converges to b, and every a_n is less than or equal to each b_n, then a is less than or equal to b. This theorem summarizes how inequalities behave with limits. #realanalysis Definition of the Limit of a Sequence:    • Definition of the Limit of a Sequence | Re...   Limit Law for Difference of Convergent Sequences:    • Proof: Limit Law for Difference of Converg...   Proof that a Constant Sequence Converges to its Constant Value:    • Proof: Constant Sequence Converges to its ...   Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu