Number Systems with Simplicity Hierarchies: A ... - Ohio University

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$Introduction to Numerical Math and Matlab ... - Ohio University$

1236 PHILIP EHRLICH DEFINITION 2. (A, +,
NUMBER SYSTEMS WITH SIMPLICITY HIERARCHIES 1237 PROPOSITION 1. (i) 0 is the simplest element of (as well as the unique root in) an s-hierarchical ordered group A, i.e., 0 ={0 o 0}A; (ii) for each element x of an s- hierarchical ordered group A, -x = {-xR I XL}A; (iii) 1 is the simplest positive element of an s-hierarchical orderedfield A, i.e., 1 ={0 I}A. 1.3. Complete s-hierarchical ordered algebraic structures. A binary tree will be said to be full if every element has two immediate successors and every chain of infinite limit length < On has an immediate successor. As Theorem 4 below makes clear, in the case of lexicographically ordered binary trees the concept of a full binary tree is intimately related to the following conception. DEFINITION 6. A lexicographically ordered binary tree (A,
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Number Systems with Simplicity Hierarchies: A ... - Ohio University

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