What Is the Most Rigorous Combinatorics Book Available?

[SrVishi]

Hi, I am trying to find a completely rigorous book on combinatorics. For example, one that states the sum and product counting principles in terms of set theory and proves them, treats permutations as a bijection from a set onto itself, etc. Many don't even explain the reasoning behind those principles, taking them as mere informal facts, so rigorous set theoretic definitions and proofs could at least help my intuition. It seems that even those that try to be rigorous don't live up to it. For example, some don't prove the pigeonhole principle, or do it with informal reasoning in terms of bins/balls. Other times, the attempts at "proofs" are just plain "handwavy." Could someone recommend me a good book? Thanks in advance for any response.

 

[micromass]

A combinatorics book isn't what you want, you want a set theory book.

 

[bacte2013]

Hi, I am trying to find a completely rigorous book on combinatorics. For example, one that states the sum and product counting principles in terms of set theory and proves them, treats permutations as a bijection from a set onto itself, etc. Many don't even explain the reasoning behind those principles, taking them as mere informal facts, so rigorous set theoretic definitions and proofs could at least help my intuition. It seems that even those that try to be rigorous don't live up to it. For example, some don't prove the pigeonhole principle, or do it with informal reasoning in terms of bins/balls. Other times, the attempts at "proofs" are just plain "handwavy." Could someone recommend me a good book? Thanks in advance for any response.

Try either Kunnen's Set Theory or Jech's Set Theory.