Now, itÕs a proper time to justify the title of this book. The fourth volume of Innovative Math represents an attempt to describe the fundamentals of TRIZ 2.0 in Òmathematical styleÓ: selecting the axioms, formulating and proving the lemmas and theorems, analyze the known TRIZ toolsÕ comprehensiveness. Of course, this is rather a parody of the mathematical style, but at least this description is a little bit more exact that just phenomenological one. The readers of this volume are those who participate in scientific development of TRIZ. This is an invitation to the new work. Now, it seems the right time to describe the innovative process with mathematical accuracy, with proofs. ThatÕs what this book is about.