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

Sometimes, ambiguities are implicitly resolved by notational convention. For example, the conventional interpretation of $a\wedge b\wedge c=a^{b^c}$ is $a^{(b^c)}$, never $(a^b)^c$, so that the expression $a\wedge b\wedge c$ is well-defined even though exponentiation is nonassociative.

© 1996-9 Eric W. Weisstein