In this paper, by using the power of nonstandard analysis tools, we review some of the standard facts on the intermediate value property (IVP) and investigates some new nonstandard developments by extending the classical definition. The notions are generalized to that of any real values; infinitesimals, infinitely close, unlimited. Finally, we give a nonstandard generalization of Sierpinski theorem. We prove that every function can be expressed as a sum of four discontinuous nonstandard functions with infinitesimal intermediate value property (IIVP).
(2016). ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY. Assiut University Journal of Multidisciplinary Scientific Research, 45(2), 35-45. doi: 10.21608/aunj.2016.221419
MLA
. "ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY". Assiut University Journal of Multidisciplinary Scientific Research, 45, 2, 2016, 35-45. doi: 10.21608/aunj.2016.221419
HARVARD
(2016). 'ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY', Assiut University Journal of Multidisciplinary Scientific Research, 45(2), pp. 35-45. doi: 10.21608/aunj.2016.221419
VANCOUVER
ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY. Assiut University Journal of Multidisciplinary Scientific Research, 2016; 45(2): 35-45. doi: 10.21608/aunj.2016.221419
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