I am reading a notes about tensor when I came across this which the notes did not elaborate more on it. As a result I dont quite understand why. Here it is : " Note that we mark the covariant basis vectors with an upper index and the contravariant basis vectors with a lower index. This may sounds counter-intuitive ('did we not decide to use upper indices for contravariant vectors?') but this is precisely what we mean with the 'different meaning of the indices' here: this time they label the vectors and do not denote their components. " I can follow except the last sentence and I do not know why. Can anyone enlighten me?