Elements of Subgroup of Dipper Semigroup are not Invertible in Dipper/Examples

Examples of Use of Elements of Subgroup of Dipper Semigroup are not Invertible in Dipper

Example: $\struct {H, +_{3, 4} }$

Consider the 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 Dipper Semigroup Example: $\struct {H, +_{3, 4} }$

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

whose identity is $4$.

But from Elements of Subgroup of Dipper Semigroup are not Invertible in Dipper, $\struct {H, +_{3, 4} }$ has no invertible elements in $\struct {N_{<7}, +_{3, 4} }$.