Original sentence: Another example would be the additive set of positive natural numbers.As the last example shows, it is possible for (S,*) to have several left identities.It is also quite possible for (S,*) to have no identity element.The absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied - so that it is not possible to obtain a non-zero vector in the same direction as the original
Edited sentence: Another example would be the additive semigroup of positive natural numbers.As the last example shows, it is possible for (S, *) to have several left identities.It is also quite possible for (S, *) to have no identity element.The absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied – so that it is not possible to obtain a non-zero vector in the same direction as the original