It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

Explains the significance of the mole as a unit of measure by showing the relationship between physical quantities and their mathematical representations. Offers a summary of the principles of metrology that make creation of physical quantities and units seem reasonable. A table of base physical quantities and units is included. (RT)

Proposes a method for dealing with units that require involvement of units of each physical quantity at every stage of a calculation. Preliminary ideas on algebra and the concept of a physical quantity, equations relating two or more units, calculations of physical quantities, and logarithms are considered. (JM)