Why they chose maximum and not minimum functions

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SUMMARY

The discussion centers on the use of maximum versus minimum functions in mathematical proofs, specifically in the context of epsilon-delta definitions. The participants highlight that while minimum functions are commonly used to approach limits, there are scenarios where maximum functions are applicable. A key point raised is the importance of understanding when to apply each function, particularly in relation to inequalities and their manipulation. The conversation references specific examples and proofs that illustrate these concepts.

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  • Understanding of epsilon-delta definitions in calculus
  • Familiarity with inequalities and their properties
  • Knowledge of mathematical proofs and logic
  • Basic proficiency in calculus concepts
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  • Research the application of epsilon-delta proofs in calculus
  • Study the properties of inequalities in mathematical analysis
  • Explore examples of maximum and minimum functions in limit proofs
  • Learn about the implications of function inversion on inequalities
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Students of calculus, mathematics educators, and anyone interested in deepening their understanding of limit proofs and the application of maximum and minimum functions in mathematical analysis.

transgalactic
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It's not clear what your question is. In the first example you give, they have [itex]|x-a||x-b|< \epsilon[/itex] in order to get |x-a| only, you have to divide both sides by |x-b| "inverting it reverses the inequality. That doesn't happen in the second example- there is no reciprocal.
 
when to use MAX when to use MIN ?
 

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