11. Ch # 2 The Real Numbers | Exercise 2.2, Question 1 to 5 | Real Analysis by Robert G Bartle

Introduction to Real Analysis by Robert G Bartle and Donald R. Sherbert.
Chapter # 2 The Real Numbers
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In this video I will discuss question number 1 to 5 of Exercise 2.2. These questions are related to absolute value of a real number. These questions are
Q#1. If a,b∈R and b≠0, show that (a)|a|=√(a^2 ) (b)|a/b |=|a|/|b|
Q#2 If a,b∈R, show that |a+b|=|a|+|b| iff ab≥0.
Q#3 If x,y,z∈R and x≤z, show that x≤y≤z iff |x-y|+|y-z|=|x-z|. Interpret this geometrically.
Q#4 Show that |x-a|≤ε iff a-ε≤x≤a+ε
Q#5 if x,y∈(a,b). Show that |x-y| is less than b-a.
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