What are some recommended books for elementary math proofs?

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SUMMARY

The discussion centers on recommended books for understanding elementary math proofs, with specific references to "Calculus" by Michael Spivak and "Introduction to Mathematical Analysis" by Tom Apostol. The user highlights a proof demonstrating that 1 is greater than 0, emphasizing the foundational nature of such proofs. Additional recommendations include "How to Read and Do Proofs" by Daniel Solow and "The Nuts and Bolts of Proofs" by Antonella Cupillari, both of which cater to beginners in mathematical proofs.

PREREQUISITES
  • Familiarity with basic mathematical operations (addition, multiplication)
  • Understanding of mathematical properties (distributive, associative)
  • Basic knowledge of mathematical proofs
  • Exposure to introductory calculus concepts
NEXT STEPS
  • Explore "How to Read and Do Proofs" by D. Solow for foundational proof techniques
  • Study "The Nuts and Bolts of Proofs" by Antonella Cupillari for practical proof strategies
  • Review "Calculus" by Michael Spivak for advanced insights into mathematical properties
  • Investigate "Introduction to Mathematical Analysis" by Tom Apostol for a deeper understanding of analysis concepts
USEFUL FOR

Students and educators in mathematics, particularly those seeking to strengthen their understanding of elementary proofs and foundational concepts in math.

Jimmy84
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I just started reading the introductory section of Spivak's calculus, and it has an introduction about the main mathematical properties; dristributive, associative etc. also how basic operations such as multiplication arises naturally from addition and division from multiplication.

What caught my attention was a proof about 1 being greater than 0. due to the fact that
n square has to be greater than 0. and since 1 square = 1, then 1 is greater than 0.

Right now I am reading Spivak and Apostol's introduction to basic math but I was wondering if there are books that deal with this kind of elementary proofs, can someone recommend me some?

I don't mean books about logic but about elementary math like the above mentioned. I am having a hard time finding any book about this subject.
 
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How to Read and Do Proofs by D. Solow

of course this is at a much more elementary level than Spivak.
 
Another is The Nuts and Bolts of Proofs, by Antonella Cupillari.
 

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