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Reading about hyperreals I learned that a serious problem with such systems is their undefinability.

So I tried to construct a definable system of hyperreals by introducing an infinitismal element $\varepsilon$ such that

$$0^\varepsilon=\frac{1}e$$ by definition.

It seems to me that such system would inevitably include divisors of zero but I am not sure.

I wonder whether such system viable and whether it in fact includes divisors of zero.

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    Have you seen [this](http://www.math.wisc.edu/~keisler/foundations.html)?2012-10-30
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    @Ian Mateus yes this is exactly what I saw before making this question.2012-10-30

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