Tree successor algebra

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Focusing on a formal theory of tree generation, this book introduces the concept of collection space, linking rooted trees to variables in sum form equations. It explores connections with number theory, linear algebra, and algebra, establishing a fundamental relationship between rooted tree generation and partition generation. A successor operator is defined, facilitating the creation of tree sequences and the infinite sequence of all rooted trees. The axiomatic system developed addresses the need for tools to solve these equations, highlighting a new branch in mathematics.