MyWikiBiz, Author Your Legacy — Wednesday June 05, 2024
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, 17:50, 28 July 2009
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− | Let <math>S\!</math> be the set of rooted trees and let <math>S_0 \subset S</math> be the 2-element subset consisting of a rooted node and a rooted edge. We may express these definitions more briefly as <math>S = \{ \operatorname{rooted~trees} \}</math> and <math>S_0 = \{ \ominus, \vert \}.</math> Simple intuition, or a simple inductive proof, will assure us that any rooted tree can be reduced by means of the axioms of the primary arithmetic either to a root node <math>\ominus</math> or else to a rooted edge <math>\vert\,.</math> | + | Let <math>S\!</math> be the set of rooted trees and let <math>S_0\!</math> be the 2-element subset of <math>S\!</math> that consists of a rooted node and a rooted edge. We may express these definitions more briefly as <math>S = \{ \operatorname{rooted~trees} \}</math> and <math>S_0 = \{ \ominus, \vert \}.</math> Simple intuition, or a simple inductive proof, will assure us that any rooted tree can be reduced by means of the axioms of the primary arithmetic either to a root node <math>\ominus</math> or else to a rooted edge <math>\vert~.</math> |
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| For example, consider the reduction that proceeds as follows: | | For example, consider the reduction that proceeds as follows: |