On page 98 of Zwiebach's book "A First Course in String Theory", the following claim is made: At each point on the worldsheet of a string there is both a spacelike and a timelike tangent vector. Professor Zwiebach acknowledges that the statement needs to be softened as follows: At each point on the worldsheet, except those points associated with the endpoints of an open string, there is both a spacelike and a timelike tangent vector. At the points associated with endpoints, there is both a spacelike and a null tangent vector. I don't understand the proof that he gives. Can someone provide me with an alternative proof, or a clearer version of his proof? Or is the theorem perhaps untrue? Are there interior points with a null tangent vector, but no timelike tangent vector?