Terminology and Notation
Jean-Robert Argand introduced the term "module", meaning 'unit of measure' in French, in 1806 specifically for the complex absolute value and it was borrowed into English in 1866 as the Latin equivalent "modulus". The term "absolute value" has been used in this sense since at least 1806 in French and 1857 in English. The notation | a | was introduced by Karl Weierstrass in 1841. Other names for absolute value include "the numerical value" and "the magnitude".
The same notation is used with sets to denote cardinality; the meaning depends on context.
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