Binoid: M = F ( N ) ⋆ := ( F ( N ) , ⋆ , N × , N ) , F ⋆ G := F i l t ( F + G ) , F , G ∈ F ( N ) {\displaystyle {}M={\mathcal {F}}(N)_{\star }:=({\mathcal {F}}(N),\star ,N^{\times },N){\text{, }}F\star G:=Filt(F+G){\text{, }}F,G\in {\mathcal {F}}(N)} .