Reclosed
Please consider re-closing this question : http://math.stackexchange.com/questions/1648838/is-it-to-the-students-advantage-to-learn-the-language-of-infinitesimals
On the one hand, the question is primarily about pedagogy, which would be a better fit for a different SE site. But, more importantly, the question is essentially a request to engage in a discussion about whether there is an "advantage" to teaching infinitesimals. This is a perfect example of a question that is primarily opinion based, and arguably "subjective and argumentative" as the former close reason said.
This kind of subjective discussion is certainly healthy for the field of mathematics, but it is not what we want on this site. The help center puts it clearly: If your motivation for asking the question is “I would like to participate in a discussion about ______”, then you should not be asking here.