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Hybrid systems modelers have become the corner stone of embedded system development, with Simulink a de facto standard and Modelica a new player. Such tools still raise a number of issues that, we believe, require more fundamental understanding. In this paper we propose using non standard analysis as a semantic domain for hybrid systems -non standard analysis is an extension of classical analysis in which infinitesimals (the ε and η in the celebrated generic sentence ∀ε∃η . . . in collegedoi:10.1109/cdc.2010.5717614 dblp:conf/cdc/BenvenisteCP10 fatcat:yzjdutqvgfa5lgphiwd5mkhxge