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The sum, difference, or product of two infinitesimals is an infinitesimal. Jerome Keisler, Foundations of infinitesimal calculus. Calculus in their last collegiate year, or as part of Theory of Functions. This indicates that such an increase in lifetime can be attributed to an interaction of the radioactive material with the subparticle field. Luxemburg, Introduction to the theory of infinitesimals, and H. The elimination of infinitesimals by the introduction of limit processes represented a great progress in foundational work (although one may again find a justification for infinitesimals as it is done today in the field of nonstandard analysis). This line element is now used to derive, by means of separation of variables, an expression that predicts the same increase in the decay time for radioactive material as that predicted by the Einstein time dilation assumption. On the one hand there was the notion of infinitesimals which embodied ‘infinity in the small’. Previously, this line element was employed to obtain, with the exception of radioactive decay, various experimentally verified special theory relativistic alterations in physical measures. The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. In this paper, using concepts from the nonstandard physical world, the linear effect line element is derived.