sentences:  To define the vector norm (and distance) in an invariant manner, one has to get square roots of scalar squares, which leads to possibly imaginary distances; see square root of negative numbers.But even for a triangle with positive scalar squares of all three sides (whose square roots are real and positive), the triangle inequality does not hold in general.Hence terms "norm" and "distance" are avoided in pseudo-Euclidean geometry, which may be replaced with "scalar square" and "interval" respectively.