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new ineguality for smarandache function

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Al and A3, A3 lies between A2 and A ~ etc. and the segmen ts AAI, AIA2, A2A3, A3A4, ... are congruent to one another. Then, among this series of points, n ot always there exists a certain point An such that B lies between A and An For example: let A be a point in deltal-fl and B a point on fl B different from P; on the line AB consider the points AI A2, A3, A4, ... in between A and B, such that AAI, AIA2, A2A3, A3A4, etc. are congruent to one another; then we find that there is no point behind B (considering the direction from A to B), because B is a limit point (the line AB ends in B). The Bolzano's (intermediate value) theorem may not hold in the Critical Zone of the Model. Can yo u readers find a better model for this anti-geometry? References: [1] Charles Ashbacher, Smarandache Geometries , <Smarandache Notions Journal>, Vol. 8, No. 1-2-3, Fall 1997, pp. 212-215. [2] Mike Mudge, A Paradoxist Mathematician, His Function, Paradoxist Geometry, and Class o f Paradoxes , <Smarandache Notions Journal>, Vol. 7, No. 1-2-3, August 1996, pp. 127-129. reviewed by David E. Zitarelli, <Historia Mathematica>, Vol. 24, No. 1,p. 114,#24.1.119,1997. [3] Marian Popescu, A Model for the Smarandache Paradoxist Geometry , <Abstracts of Papers Presented to the American Mathematical Society Meetings>, Vol. 17, No.1 Issue 103, 1996, p. 265. [4] Florentin Smara ndach e, Colle cted Papers (Vol. II), University o f Kishinev Press, Kishinev, pp. 5-28, 1997. [5 ] Florentin Smarandache, Paradoxist Mathematics (lecture), Bloomsburg University, Mathematics Department, PA, USA, November 1985. 6

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