Not to detract from your point, but you don't need the expansion for that. Directly substituting 𝟏 in the definitional equation works just fine: L a = 𝟏

Not to detract from your point, but you don't need the expansion for that. Directly substituting 𝟏 in the definitional equation works just fine: L a = 𝟏 + a × (L a) L 𝟏 = 𝟏 + 𝟏 × (L 𝟏) L 𝟏 = 𝟏 + (L 𝟏) L 𝟏 = 𝟏 + 𝟏 + 𝟏 + 𝟏 + 𝟏 + 𝟏 + ... ℕ = 𝟏 + 𝟏 + 𝟏 + 𝟏 + 𝟏 + 𝟏 + ... The final expansion is worth writing, however, since it notes how there are unboundedly many naturals, each a different component in this infinite disjoint sum.