Non-orientable genus of Unknot and it's uniqueness

Question

In the book "Topology Now!" by Robert Messer one of the practice problem suggests, " One could define the nonorientable genus of a knot to be zero for the trivial knot, and for any other knot K to be the smallest number p such that the surface formed by taking; the connected sum of p projective plans and removing one disk will span K "
Trivial knot or unknot is assigned zero beacuse it bounds a mobius band?? As in the orientable context unknot is the only knot that bounds a disk.

Is unknot the only knot that bounds a mobius band??

Answer 1

Just give the Möbius band another two half turns (three half turns total) and it's still a Möbius band, but now with a trefoil as its boundary. One may of course repeat this procedure to get any $(2,n)$-torus knots.