It is interesting to note that no combination of knots can cancel each other out. When one looks at the additive property of the genus, this can be understood logically. The genus of the sum of two knots, g(K + L), is equal to the sum of the genuses, g(K) + g(L). Also, the genus of the unknot is 0, and a genus of 0 is the unknot. Therefore, if a non-trivial knot is to cancel out another non-trivial knot, either one of the genuses has to be negative or they must both be zero. A negative genus does not make sense, and a genus of zero signifies the unknot. Thus, no group of non-trivial knots can be combined to obtain the unknot.
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