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

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

1254 PHILIP EHRLICH The nature of the system of omnific integers of a nontrivial initial subgroup of No is greatly clarified by the following theorem, the nonroutine portion of which follows immediately from Conway's proof of Theorem 31 of [7]. THEOREM 20. If A is a nontrivial initial subgroup of No, then Oz (A) is the subclass of all x c A such that x Zcow . ac, a
apt . NUMBER SYSTEMS WITH SIMPLICITY HIERARCHIES 1255 together <strong>with</strong> other familiar theorems concerning ordinals leads to the following well-known theorem due to Cantor: Every ordinal a < On has a unique Cantor Normal Form, i.e., a unique representation of the form E09c *oa c aa a
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Number Systems with Simplicity Hierarchies: A ... - Ohio University

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