Identity of Subgroup of Dipper Semigroup is not Identity of Dipper/Examples
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Examples of Use of Identity of Subgroup of Dipper Semigroup is not Identity of 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 $4$.
We have that:
- $0 +_{3, 4} 4 = 4$
and so $4$ is not the identity of $\struct {N_{<7}, +_{3, 4} }$.