"odd + odd doesn't equal even?"

This subgroup gives us two cosets: $0 + 2\\mathbb Z$ and $1 + 2\\mathbb Z$ \(remember that $+$ is the group operation in this example\), which are the elements of our quotient group\. We will give them their conventional names: $\\text{even}$ and $\\text{odd}$, and we can apply the coset multiplication rule to see that $\\text{even}+ \\text{even} \= \\text{even}$, $\\text{even} + \\text{odd} \= \\text{odd}$, and $\\text{odd} + \\text{odd} \= \\text{odd}$\.

odd + odd doesn't equal even?