Real analysis

Awesome course notes

Real analysis playlists:

• Winston Ou
• Bill Kinney
• BriTheMathGuy
• Artem Chernikov
• Chris Staecker
• Michael Penn
• Drew Pass

If a subset of the real numbers has a supremum or infimum, then the supremum or infimum is unique.

70598Proof: Supremum and Infimum are Unique | Real Analysis

Wrath of Math

The limit of a sequence, when it exists, is unique.

70500Proof 4.1: Unique Limit of a Sequence

CosmoLearning

70501The Limit of a Sequence is Unique Proof

The Math Sorcerer

70499Limits are unique

Dr Peyam

70502The Limit of a Sequence is unique

Elliot Nicholson

70129When a limit exists, It is Unique - Proof

Polar Pi

Textbooks

• Real Variables with Basic Metric Space Topology
  by Robert B. Ash
  Read now
• Basic Real Analysis
  by Anthony W. Knapp
  Read now
• Advanced Real Analysis
  by Anthony W. Knapp
  Read now
• Introduction to Real Analysis
  by William F. Trench
  PDF
• Basic Analysis I: Introduction to Real Analysis
  by Jiri Lebl
  PDF
• Basic Analysis II: Introduction to Real Analysis
  by Jiri Lebl
  PDF
• An Introductory Single Variable Real Analysis: A Learning Approach through Problem Solving
  by Marcel B. Finan
  PDF
• Solution Manual to An Introductory Single Variable Real Analysis: A Learning Approach through Problem Solving
  by Marcel B. Finan
  PDF
• Real Analysis
  by Andrew M. Bruckner, Judith B. Bruckner, and Brian S. Thompson
  PDF
• Elementary Real Analysis
  by Andrew M. Bruckner Judith B. Bruckner Brian S. Thompson
  PDF
• Mathematical Analysis I
  by Elias Zakon
  PDF
• Mathematical Analysis II
  by Elias Zakon
  PDF
• Advanced Calculus
  by Lynn H. Loomis and Shlomo Sternberg
  PDF
• One Variable Advanced Calculus
  by Kenneth Kuttler
  PDF
• Introduction to Mathematical Analysis I
  by Beatriz Lafferriere, Gerardo Lafferriere, and Nguyen Mau Nam
  PDF
• A ProblemText in Advanced Calculus
  by John M. Erdman
  PDF
• Companion to Real Analysis
  by John M. Erdman
  PDF