What's the best discrete mathematics textbook?

AI Thread Summary
The discussion centers on the best discrete mathematics textbooks, highlighting "Discrete Mathematics and Its Applications" by Kenneth H. Rosen and "Discrete Mathematics with Applications" by Susanna S. Epp as popular choices. Concerns are raised about their length and perceived lack of rigor, comparing them to Stewart’s calculus. The need for a more rigorous alternative is expressed, with a recommendation for Biggs' first edition of "Discrete Mathematics" as a solid introductory text. The second edition of Biggs' book is criticized as being less suitable. Overall, the search for a rigorous discrete mathematics textbook continues.
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Apparently everyone uses either Discrete Mathematics and Its Applications by Kenneth H. Rosen or Discrete Mathematics with Applications by Susanna S. Epp. Are these really the best ones? Both are very long texts which make me think they're not rigorous and they're descriptive like Stewart’s calculus for example. Is there a discrete math text written rigorously? I appreciate any comment. Thanks in advance.
 
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For a good introduction, I favour Biggs' Discrete Mathematics, the first edition (the second is cr**; for morons only).
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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