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In the present paper, the problem of defining continuity and scontinuity as a galaxy of hyperreal function is discussed. Our attempt is based on the fact that monads are subsets of some galaxies. New results are obtained, with nonstandard variables, related to a new extension of the continuity notion.

The aim of this paper is to establish a new method for calculating generalized curvature and generalized torsion. This method depends on at least three points infinitely close to the considered point. The established method is characterize from other methods by using only dot and cross product of vectors combined from this points, without any parameter that interacts in the defined curve by using some concepts of nonstandard analysis given by Robinson A. and axiomatized by Nelson E.

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The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, A. and axiomataized by Nelson, E. to prove some theorems concerning the approximation of integrals and the convergence of sequences and series.