Identity of Subgroup of Big Dipper Semigroup is not Identity of Big Dipper/Examples/(m, n) = (3, 4)

Examples of Use of Identity of Subgroup of Big Dipper Semigroup is not Identity of Big Dipper
Consider the big dipper semigroup $\struct {N_{<7}, +_{3, 4} }$.

Let $H = \set {x \in \N: 3 \le x < 7} = \set {3, 4, 5, 6}$.

From Existence of Subgroup of Big Dipper Semigroup Example: $\struct {H, +_{3, 4} }$


 * $\struct {H, +_{3, 4} }$ is a subgroup of $\struct {N_{<7}, +_{3, 4} }$

whose identity is $4$.

We have that:
 * $0 +_{3, 4} 4 = 4$

and so $4$ is not the identity of $\struct {N_{<7}, +_{3, 4} }$.