Left and Right Hand Limits Exist in Real Analysis: A Tutorial

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SUMMARY

The discussion focuses on the concept of left and right hand limits in the context of real analysis, specifically referencing Royden's "Real Analysis." The user seeks clarification on the notation regarding the existence of limits as x approaches a point c from the left (c-) and the right (c+). The conclusion is that demonstrating the existence of these limits is indeed the correct approach, paralleling concepts learned in calculus.

PREREQUISITES
  • Understanding of limit notation in calculus
  • Familiarity with the concepts of left-hand and right-hand limits
  • Basic knowledge of real analysis principles
  • Experience with Royden's "Real Analysis" text
NEXT STEPS
  • Study the definitions and properties of limits in real analysis
  • Explore examples of left-hand and right-hand limits in various functions
  • Review theorems related to limit existence in Royden's "Real Analysis"
  • Practice problems involving limit calculations and their implications
USEFUL FOR

Students of real analysis, educators teaching calculus concepts, and anyone looking to solidify their understanding of limits in mathematical analysis.

futurebird
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This is a simple question. I need to know if I'm reading the notation correctly.

"Show that for each c in (a,b) the limit f(x) exists as x --> c- and as x --> c+."

This is in Royden's Real Analysis.

What I'm going to do is show that the left and right hand limits exist... right? Just like in Calc. I 15 years ago... like I remember any of this... LOL.

But that's what I'm supposed to do here? Correct?
 
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