Continuity of |f|: Examples w/ Discontinuity at 0

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SUMMARY

The discussion focuses on identifying a function f that is discontinuous at 0 while its absolute value, abs(f), remains continuous at 0. A common example provided is a step function, which demonstrates this property effectively. Participants emphasize the need for clear examples and hints to understand the concept better. The exploration of discontinuous functions highlights the nuances of continuity in mathematical analysis.

PREREQUISITES
  • Understanding of continuity and discontinuity in functions
  • Familiarity with absolute value functions
  • Basic knowledge of step functions
  • Concepts of mathematical analysis
NEXT STEPS
  • Research examples of step functions and their properties
  • Study the definition and implications of continuity in mathematical analysis
  • Explore the relationship between discontinuous functions and their absolute values
  • Learn about piecewise functions and their continuity characteristics
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Mathematics students, educators, and anyone interested in the properties of functions and continuity in mathematical analysis.

sean/mac
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Give an example of a function f which is discontinuous at 0 yet abs(f ) is continuous at 0

i have tried for an hour or so trying to think of one, even hints would be helpful
 
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I can think of a very trivial example... sort of like a step function.
 

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