I’m trying to prove that if a set $S$ is dense in the even subalgebra $A^+$ of a $\mathbb{Z}_2$-graded algebra $A$ then $S$ is dense in the algebra $A$. But since density is not transitive, I don’t know how to proceed.
¿How can I prove this assertion?
Thank you!
Note: Here $\mathbb{Z_2}$ is the boolean algebra $\{0,1\}$.