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I want to read some modern literature on elementary Mathematics. I already have old literature, but I am not aware of the modern terminology. I do not want abstract algebra, number theory or linear algebra books/literature etc. I want some modern book/literature which explains only elementary stuff. By elementary I mean the book should explain:

  1. What is Math/algebra and what is its purpose,

  2. Natural numbers and operations upon them,

  3. Then the book should explain in detail about commutative, associative and distributive laws of Natural numbers,

  4. After this the book should explain why and how we define 0, negative, rational and irrational numbers from both pure and applied point of views,

  5. The book should explain the laws(definitions) of commutative, associative and distributive laws upon 0, negative, rational and irrational numbers from both pure and applied point of views. And why the rules of multiplication, addition, division and subtraction for them(0, negative, rational and irrational numbers) are defined the way they are from both pure and applied point of views.

This is it, I do not want to study anything further, like quadratic equations, exponents etc. Let me reemphasize I need modern literature only, that is the one which uses the terminology used by present mathematicians, not the outdated stuff.

Thanks in advance.

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  • $\begingroup$ Have you tried the relevant articles in Wikipedia? You can even select the print-friendly option and print them out. $\endgroup$
    – Mike Jones
    May 13 '17 at 18:30
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The first chapter or so of Spivak's excellent Calculus is perhaps what you're looking for.

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  • $\begingroup$ No this is not what I am looking for. It doesn't explain things from applied mathematical point of view. e.g. what are the benifits of defining negative number aside from the fact that they provide a solution to the equation of sort $a+x=a$. why should multiplication always be commutative for all kinds of numbers(say irrationals) etc etc. $\endgroup$
    – user103816
    Oct 31 '14 at 16:13
  • $\begingroup$ In the above comment I meant $a+x=b$ where $b<a$. $\endgroup$
    – user103816
    Nov 1 '14 at 4:27

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