Single Component Vectors

Sports score couplets are vectors. They have at least one component and a particular order. The specific order isn’t the criteria; that there is an order is the criteria.

However that doesn’t mean that vectors require two or more components. A single component can be a vector.

Example: score differentials. Last week JMU lost 38-45 to Georgia Southern. The differential was -7. That differential is a vector.

It’s got at least one component, the 7, with a particular order. The order is the order of the two teams. The differential could be +7, with direction reversed but magnitude the same, provided the order is reversed. +7 would be the Georgia-JMU differential. Single component, particular order.

Put another way, a vector is an amplitude and a direction. The 7 is the amplitude, the +/- is the direction.

This is why all negative numbers are vectors. They address a state of change, and the order of the components changing is the order of this small vector.