MyWikiBiz, Author Your Legacy — Wednesday May 29, 2024
Jump to navigationJump to search
No change in size
, 18:06, 19 August 2008
Line 126: |
Line 126: |
| <br> | | <br> |
| | | |
− | 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 \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> |
| | | |
| For example, consider the reduction that proceeds as follows: | | For example, consider the reduction that proceeds as follows: |