An involutive monoid is an Involutive Semigroup ( S , ⋆ , ( − ) † ) 𝑆 ⋆ superscript † (S,\star,(-)^{\dagger}) that has an Identity Element ε 𝜀 \varepsilon with ε † = ε superscript 𝜀 † 𝜀 \varepsilon^{\dagger}=\varepsilon .