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

In summary, the conversation is about a person who is struggling with a question in Spivak's Calculus and is seeking guidance on how to approach it. They mention that they are not a native English speaker and have not had experience with proof-based mathematics before. They also mention that they need to use four given properties to prove others, which they did not include in the provided image. They receive clarification and feel more confident about their direction.
  • #1
usn7564
63
0

Homework Statement


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

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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  • #2
usn7564 said:

Homework Statement


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

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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  • #3
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.
 

1. What are the properties that can be deduced as theorems in Spivak's book?

Spivak's book covers a wide range of mathematical topics, including calculus, linear algebra, and differential geometry. As such, there are many different properties that can be deduced as theorems. Some examples include the fundamental theorem of calculus, the Pythagorean theorem, and the Gauss-Bonnet theorem.

2. How are these properties deduced as theorems in Spivak's book?

Spivak uses rigorous mathematical proofs to deduce these properties as theorems. He starts with basic definitions and axioms, and then builds upon them to logically prove the desired property.

3. Can these theorems be applied to real-life problems?

Yes, many of the theorems discussed in Spivak's book have real-life applications. For example, the fundamental theorem of calculus is essential for understanding and solving problems in physics and engineering.

4. Is Spivak's book suitable for beginners in mathematics?

No, Spivak's book is not recommended for beginners in mathematics. It is more suitable for students who have a strong foundation in calculus and are looking to deepen their understanding of mathematical concepts.

5. Are there any prerequisites for understanding the theorems in Spivak's book?

As mentioned before, a strong understanding of calculus is necessary to fully grasp the theorems in Spivak's book. Additionally, some knowledge of linear algebra and geometry may also be helpful in understanding certain theorems.

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