I'm reading a differential geometry book named "Elementary geometry of differentiable curves: An undergraduate introduction" written by Gibson.
I'm on page 2. On that page, 4 properties of scalar product(dot product) of vectors are given.
One of them is:
I know the proof of this and the proof shows that the statement is true for
I accept this.
But if isn't it definite that has to be equal to and not greater than ?
Can anyone find a such that when then is greater than ?
Why did the author said that ? Why did he mention greater and equal, and not just equal to ?