DIMENSIONALITY

 Definition: An expression of measurement without units.

 Context: A quantity is a value with an associated unit of measure. 32 Fahrenheit, 0 Celsius, \$100 USD, and 10 reams (of paper) are quantities. Equivalence between two units of measure is determined by the existence of a quantity preserving one-to-one correspondence between values measured in one unit of measure and values measured in the other unit of measure, independent of context, and where characterizing operations are the same. Equivalent units of measure in this sense have the same dimensionality. The equivalence defined here forms an equivalence relation on the set of all units of measure. Each equivalence class corresponds to a dimensionality. The units of measure "temperature in degrees Fahrenheit" and "temperature in degrees Celsius" have the same dimensionality, because for each value measured in degrees Fahrenheit there is a value measured in degrees Celsius with the same quantity, and vice-versa. The same operations may be performed on quantities in each unit of measure. Quantity preserving one-to-one correspondences are the well-known equations C = (5/9)*(F - 32) and F = (9/5)*(C) + 32.

 Source Publication: ISO/IEC FDIS 11179-1 "Information technology - Metadata registries - Part 1: Framework", March 2004.

 Cross References: Dimension ISO / IEC 11179 Unit of measure