Calculus Michael Spivak 3th ed. Pag 46: Function as a rule

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Discussion Overview

The discussion revolves around a specific passage from page 46 of Michael Spivak's third edition of a calculus textbook, focusing on the definition of a function as a rule. Participants examine a potential typo in the text and its implications for understanding functions.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • One participant notes that the text suggests a function is a rule, leading to the conclusion that two expressions for f(x) are different, which they find problematic.
  • Another participant agrees that it appears to be a typo and suggests simply correcting it and moving on.
  • A different participant mentions having the first edition of the book, which does not contain the typo, implying that newer editions may introduce errors.
  • A later reply introduces a philosophical comment on entropy, possibly reflecting on the nature of changes in published works.

Areas of Agreement / Disagreement

Participants express differing views on the presence of a typo, with some agreeing it is a mistake while others highlight the inconsistency between editions. The discussion remains unresolved regarding the implications of this potential typo on the understanding of functions.

Contextual Notes

Limitations include the lack of clarity on how the definition of a function as a rule may vary between editions and the implications of these variations on mathematical understanding.

xorg
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Pag 46 says:
NGw7QSt.png

He begins to do a rethink about what is a function.
Function is a rule? If it is a rule then:
f(x) = x²
and
f(x) = x² +3x + 3 -3(x+1)
are different. But that was not what we wanted.

But he rewrites, this way:
f(x) = x²
and
f(x) = x² +3x +3 -c(x+1)

Apparently this was a small mistake.

I would like to hear the opinion of colleagues. Thank you.
 
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Looks like a typo yes. Every book has a few, you should just correct it as you did and carry on.
 
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I have the first edition, which doesn't have the typo. Sometimes books get worse instead of better when new editions are published. :frown:
 
Last edited:
Ah, entropy...
 

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