Here, particularly I'm looking for a book which starts with set theory and constructs real numbers on that basis (it should include Dedekind cut). Other than Landau's book.

Edit: Thank you all in comments for your suggestions. I found this book 'From natural numbers to quaternions' by Kramer and Pippich (thought bit advanced atleast for me but very readable), Elementary Set theory by Enderton (Thanks to Asaf Karagila), Goldrei's book is also really good (Thanks to palmpo). Last two books I mentioned do both jobs of constructing numbers and introducing set theory really well.

  • $\begingroup$ Bourbaki, if you have enough patience. $\endgroup$ – Cave Johnson Jun 2 '18 at 4:34
  • $\begingroup$ @CaveJohnson What's the title of that book? I've almost completed naive set theory, it doesn't explain construction of real numbers. Any recommendation combining both of these aspects (set theory, number construction). $\endgroup$ – Manny46 Jun 2 '18 at 4:40
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    $\begingroup$ One book that gets to Dedekind's construction of the real numbers early on is Dasgupta's Set Theory, Springer, 2014. Moschovachis's Notes on Set Theory has an appendix on the real numbers. $\endgroup$ – Fabio Somenzi Jun 2 '18 at 4:51
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    $\begingroup$ Maybe John Stillwell's The Real Numbers: An Introduction to Set Theory and Analysis? $\endgroup$ – Hans Lundmark Jun 2 '18 at 8:47
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    $\begingroup$ Try Goldrei's Classic Set Theory, it constructs real numbers from rationals, rationals from integers, etc. until they have to construct sets from set theory. $\endgroup$ – palmpo Jun 2 '18 at 22:47

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