An expression is called well-defined (or Unambiguous) if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be well defined or to be Ambiguous.

For example, the expression (the Product) is well-defined if , , and are integers. Because integers
are Associative, has the same value whether it is interpreted to mean or . However, if , ,
and are Cayley Numbers, then the expression is *not* well-defined, since
Cayley Number are not, in general, Associative, so that the two interpretations and
can be different.

Sometimes, ambiguities are implicitly resolved by notational convention. For example, the conventional interpretation of is , never , so that the expression is well-defined even though exponentiation is nonassociative.

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1999-05-26