Authors: Robert S. Miller
This paper explores the Null Algebra and traditional Algebra resolutions for the complex number . It explains the apparent differences between the Null Algebra resolutions, and thoseof traditional Algebra, which uses the substitution i=e^(i π/2) . The methods shown herein explore the full set of subspace equations implied by a given equation whose output results in for a specific input. It is shown that the values obtained from the various possible resolutions of are found on some aspect of the given equation, or its expanded subspace equation sets. It shows equals -1 and +0.20788. It is assumed the reader has read and understood Null Algebra, as well as Null Algebra Extensions I and II in addition to standard Algebra and Trigonometry. The Null Algebra texts are available for download at (https://vixra.org/abs/2103.0131), (https://vixra.org/abs/2206.0135) and (https://vixra.org/abs/2304.0205). If you have not yet read these texts and attempted the examples contained therein for yourself it is highly suggested you do so before reading further as some concepts explained in detail there, are given only cursory review here. Without reading these prerequisites you may not fully understand the reasoning behind logic used in the equations of this text. This version of the paper is submitted as a correction to original submission on 9 August 2023 of the same title. The explanation of how various solutions were arrived at, and the graphs of those solutions plotted, did not include a necessary step addressing ⨁ numbers, raised to ⨁ exponents. Those errors have been corrected in this paper.
Comments: 23 Pages. This document replaces the paper of the same title published 9 Aug 2023.
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[v1] 2023-08-09 22:17:17
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