Difference between revisions of "Associative property"
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Revision as of 16:09, 15 August 2006
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A binary operation is said to be associative if
for all
. Associativity is one of the most basic properties an operation can have.
For instance, the operation "" on the real numbers is associative because
for all real numbers
.
If we have an operation which is written between its arguments (like "
" or "
" conventionally are), associativity tells us that we may write
unambiguously -- it does not matter which pair we combine first.
For a non-example, consider the operation given by
. This operation is not associative because
while
and those expressions are not equal for all choices of
(in particular, they differ whenever
).