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I've been reflecting on fundamental mathematics that I gloss over in
my introductory physics classes, and it occurred to me that there are
actually three types of scalars that we use in introductory physics:
1) Never-negative scalars, like mass or length or distance.
2) Scalars which can be negative, and the zero is significant: like
charge or flux or current, or changes in temperature, or vector
components.
3) Scalars which can be negative, and the zero is not significant:
like temperature (in Celsius) and potential energy.
More importantly, are there NAMES for these three categories?
They can be broken up even further if one has a mind:
1a) Quantities like mass or length or duration, which can be added and
subtracted directly.
Too many categories may be more confusing than helpful, however.