Hello! I am trying to figure out why the Euler characteristic of the Möbius strip is 0

$\displaystyle \chi(Möbius)=1-1+0$

It indicates that the Möbius strip must have one vertix and one edge....but I dont see it....Can someone explain it to me?

If we for example want to calculate the E.C for a loop. How can a regular loop have two edges? (inside and outside)???? How many vertices will it have then?

Thank you