| 11. | This is a group with identity element, and group operations such as }.
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| 12. | An unknot is the identity element with respect to the knot sum operation.
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| 13. | Associativity and identity element axioms follow from the properties of integers.
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| 14. | The identity element of the monoid is the empty list, " nil ".
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| 15. | The identity element in the cycle graphs is represented by the black circle.
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| 16. | It is also quite possible for to have " no " identity element.
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| 17. | Each subgroup contains exactly one idempotent, namely the identity element of the subgroup.
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| 18. | Groups with intrinsically " n "-ary operations do not have an identity element.
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| 19. | Overriding is an associative operation; it has the empty function as an identity element.
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| 20. | Zero is the additive identity element of the recursively defined.
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