Addition on Numbers has no Zero Element
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On all the number systems:
|\(\ds \forall n \in \F: \, \)||\(\ds n + z\)||\(=\)||\(\ds z\)|
|\(\ds \leadsto \ \ \)||\(\ds n\)||\(=\)||\(\ds 0\)||subtracting $z$ from both sides|
As $n$ is arbitrary, and therefore not always $0$, it follows there can be no such $z$.