Could anyone suggest books on Mathematical/Real Analysis that construct natural numbers through sets not Peano axioms?
I find construction of natural numbers through sets more convenient. So I thought that book that uses sets, might be easier for me to understand than Peano based one.
I think that you should turn more to Set Theory / Logic books than Real analysis books.
One example is Basic set theory from Azriel Levy. What you're looking for is the definition of ordinals and especially finite ordinals.