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Answer : Scalar quantities can be negative. Instead of saying "scalar quantities have only magnitudes," a better description might be that a scalar quantity can be described using only one number per point in space. That number may be positive or negative. In contrast, a vector quantity cannot be described using only one number per point in space. In 3-d space, we need 3 numbers per point in space to describe a vector quantity. The word "magnitude," whether applied to a scalar or a vector or anything else, normally refers to a non-negative number. It is sometimes used to refer to the absolute value of a scalar, and sometimes used to refer to the norm (e.g., length) of a vector. In summary, this is how the words are typically used: Scalar typically refers to a single element of a number field (or a single element per point in space), such as a real number (which can be positive or negative) or even a complex number (this is common in the context of q...

Answer : Any mathematical notation is ok as long as it is common knowledge in your community. For instance, I believe I fully understand the meaning of the ≈ \approx ≈ symbol. However, I haven't ever seen the second symbol you provided. To be on the sure side you should provide a definition of any relation symbol you don't consider to be common knowledge. This may happen as a short remark ("..., where ≈ \approx ≈ denotes ...") or maybe as a table of the used symbols in the front matter of your work. As with any definition in mathematics, there is no right or wrong in the symbol/notion/etc. you use, only proper or unsound definitions. Also: When in doubt, use the symbol that is used more commonly in the standard textbooks of your field. There is no benefit in being avant-garde at notation. While it is certainly true that with the proper definition there is now 'wrong' notation, perhaps it should be mentioned that some notation is more suggestive and/o...