Editing Dual number (section)

==Superspace==
Dual numbers find applications in [[physics]], where they constitute one of the simplest non-trivial examples of a [[superspace]]. Equivalently, they are [[Grassmann number|supernumbers]] with just one generator; supernumbers generalize the concept to {{mvar|n}} distinct generators {{mvar|ε}}, each anti-commuting, possibly taking {{mvar|n}} to infinity. Superspace generalizes supernumbers slightly, by allowing multiple commuting dimensions.

The motivation for introducing dual numbers into physics follows from the [[Pauli exclusion principle]] for  fermions. The direction along {{mvar|ε}} is termed the "fermionic" direction, and the real component is termed the "bosonic" direction. The fermionic direction earns this name from the fact that [[fermion]]s obey the Pauli exclusion principle: under the exchange of coordinates, the quantum mechanical wave function changes sign, and thus vanishes if two coordinates are brought together; this physical idea is captured by the algebraic relation&nbsp;{{math|''ε''<sup>2</sup> {{=}} 0}}.