Working through spivak's calculus

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    Calculus
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Homework Help Overview

The discussion revolves around solving problems from Spivak's calculus text, specifically focusing on the concepts of maximum and minimum values of numbers. Participants express challenges in understanding the proofs and reasoning behind the formulas presented in the exercises.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants share their experiences with specific problems, particularly problem 13, and discuss the difficulty of deriving formulas for max and min functions. Questions arise about the reasoning behind checking different cases and the validity of their approaches.

Discussion Status

Some participants have offered guidance on how to approach the proofs by considering different cases. There is an ongoing exploration of the formal structure of proofs, with some expressing uncertainty about the rigor required in their explanations.

Contextual Notes

Participants note that Spivak's exercises can be quite challenging and that formal proofs may not be necessary for all problems in the book. There is mention of additional resources for learning about proofs, suggesting a mix of self-study and community support.

  • #31
Shylock said:
and does that that mean that the formula for max(x,y,z) =

x + (y+z + ly -zl)/2 ?

See for yourself: try (x,y,z) = (1,2,2).

Anyway, max(x,y,z) = max(x,max(y,z)) = (1/2)*[x + max(y,z) + |max(y,z) - x|]. Now substitute the expression for max(y,z).


RGV
 

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