A Brief Demonstration that:
 Zero and Plus One are Equivalent
 and are singularities related to, respectively, the Infinitesimal and the Infinite
 It is well known that Zero, "0," and Plus One, "+1," possess characteristics that are similar to one another; and, characteristics that are, also, different from all the other integers.  (That is: the results of being multiplied or divided by themselves are different than that for all other integers; Plus One is a factor for every prime number; all integers divided by Zero are equivalent, and so on.)  The reason for these unique characteristics is that these integers are related to the singularity . . . Infinity. Zero is related to the infinitesimal; and, less intuitively, Plus One is related to the infinite; Oneness is defined as a singularity that can be neither divided nor added to.  It is axiomatic, by definition, that there can be only one singularity, which is a limit beyond Reality that can only be approached.  Therefore, if Zero and Plus One are so related to the infinitesimal and the infinite; then, at their limits, they must be equivalent . . . equal to one another. Following is a demonstration of Plus One's relationship to the infinite as derived from the integer values of the Brunardot factor, "F," (ni2 - ni), which factor, most importantly, is salient to all Natural Ellipses.
 F = ni2 - ni The Brunardot factor (ni is any integer).
 Let, a = b a or b are any equivalent integers.
 Then, a2 - a = b2 - b; The Natural Formula.
 a2 - b2 = a - b;
 (a + b)(a - b) = a - b;
 a + b = 1; (After a division by Zero (a - b).
 Thus, a = -b + 1; and,
 b = -a + 1;
 Also, a = -a + 1; and,
 b = -b + 1.
 Thus, when, a (or b) is any integer (including zero), b (or a) is equal to a negative integer of the same value (a or b's "mirror image") plus one.  (That is, in accordance with the above Natural Formula: -5 = +6, -7 = +8, 9 = -8, 0 = +1, and so on.)
 Thus, 2a = 1; and,
 2b = 1;
 Thus, 2nn = 1 is the Conceptual Theorem (nn is any Natural number).
 Let, a (or b) be any Natural number approaching the infinite;
 Then, 2a (or 2b), which equals 1, must, also, approach the infinite along with 1, and,
 Also, it is axiomatic that Zero is at the infinitesimal limit.
 And, the infinitesimal and the infinite are the singularity: Infinity.
 Q.E.D. Zero and Plus One are, respectively, related to the infinitesimal and the infinite . . . Infinity; and thus, they are equivalent.
 The Conceptual Theorem, 2nn = 1, relates to the universality and omnipresence of the wave forms of Pulsoids and Oscilloids, which are ellipsoids that are derived from the Brunardot factor, ni2 - ni. The mathematical occurrences, described herein, are derived from the manipulations of division by Zero.  Such occurrences cannot be ignored, as is, often, the usual procedure in conventional mathematics; the meanings of these occurrences, as are clearly shown by Natural Ellipses, must be interpreted.
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