One interesting case of this is the concept of dual numbers [1], where you have the symbol \epsilon !=0 but (\epsilon)^2 = 0.
It seems contradictory, but the resulting theory is very useful for automatic differentiation [2] and for mechanics (dual quaternions) [3].
[1]: https://en.m.wikipedia.org/wiki/Dual_number
[2]: https://book.sciml.ai/notes/08-Forward-Mode_Automatic_Differ...