Show that [properties] can be deduced as a theorems, Spivak

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SUMMARY

The discussion revolves around a homework problem from Spivak's "Calculus, 3rd ed." that requires proving certain properties as theorems. The user expresses confusion about how to approach the problem, particularly in demonstrating that the four properties must apply without contradiction. Key insights include the need to reference properties listed on pages 10-12 of the book and the importance of understanding proof-based mathematics to tackle similar questions effectively.

PREREQUISITES
  • Understanding of mathematical proofs and logic
  • Familiarity with Spivak's "Calculus, 3rd ed."
  • Knowledge of the specific properties outlined in the textbook (pages 10-12)
  • Basic proficiency in English mathematical terminology
NEXT STEPS
  • Study the properties listed on pages 10-12 of Spivak's "Calculus, 3rd ed."
  • Learn techniques for constructing mathematical proofs
  • Practice solving proof-based problems in calculus
  • Explore resources on logical reasoning in mathematics
USEFUL FOR

Students beginning their journey in proof-based mathematics, particularly those studying calculus and using Spivak's textbook, as well as educators seeking to guide learners through foundational concepts in mathematical reasoning.

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Homework Statement


http://desmond.imageshack.us/Himg228/scaled.php?server=228&filename=theorem.png&res=landing

Picked up Spivak's Calculus, 3rd ed. and just started. Got to this question and I'm honestly not sure how to start, I looked in the answer book which didn't really clue me in any more.
If I understand the question it wants me to work within the four properties and show that there is no contradiction/they all have to apply? Not a native English speaker so I haven't had maths in English but that's what I got from it.

More interested in how to approach it rather than answers, would assume there's coming a lot more similar questions. Not really done any proof based maths up until now.
 
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usn7564 said:

Homework Statement


http://desmond.imageshack.us/Himg228/scaled.php?server=228&filename=theorem.png&res=landing

Picked up Spivak's Calculus, 3rd ed. and just started. Got to this question and I'm honestly not sure how to start, I looked in the answer book which didn't really clue me in any more.
If I understand the question it wants me to work within the four properties and show that there is no contradiction/they all have to apply? Not a native English speaker so I haven't had maths in English but that's what I got from it.

More interested in how to approach it rather than answers, would assume there's coming a lot more similar questions. Not really done any proof based maths up until now.

P10-P12 are properties given in the book previously(which you haven't included). You need to prove those properties using the given new ones.
 
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Ah, Christ, no wonder I didn't get it even with the answers in front of me. Know what direction I'm heading now at least, ta.
 

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