Proposal: Make dice a synonym of probability. All problems about this are sure to be about expected value or probability.
For the mods: Make gambling a synonym of probability. I said "for the mods" because gambling already has a synonym.
I'm not too keen about the birthday tag; something like calendar might be more suitable, unless one has a better name for the tag we can assign to calendrical questions.
[EDIT: I know what the notation means, and I can easily show that $x=\epsilon \otimes 1 + 1\otimes \epsilon$ satisfies $x^3=0$ but $x^2 \neq 0$. That's not what this question is about. It might be better to restrict the question to Synthetic Differential Geometry where it makes more sense. There ...
Here is a link to a long discussion regarding generalization of $\operatorname{sign}z$ function to dual numbers. There are basically two proposed versions: $\operatorname{sign}(a+\varepsilon b) = \operatorname{sign}(a) + 2 b \delta(a) \varepsilon$ - proposed by user M.G. in their answer. $\oper...
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