Editing Tuple (section)

==Properties==
The general rule for the identity of two {{math|''n''}}-tuples is
: <math>(a_1, a_2, \ldots, a_n) = (b_1, b_2, \ldots, b_n)</math> [[if and only if]] <math>a_1=b_1,\text{ }a_2=b_2,\text{ }\ldots,\text{ }a_n=b_n</math>.

Thus a tuple has properties that distinguish it from a [[Set (mathematics)|set]]:
# A tuple may contain multiple instances of the same element, so <br/>tuple <math>(1,2,2,3) \neq (1,2,3)</math>; but set <math>\{1,2,2,3\} = \{1,2,3\}</math>.
# Tuple elements are ordered: tuple <math>(1,2,3) \neq (3,2,1)</math>, but set <math>\{1,2,3\} = \{3,2,1\}</math>.
# A tuple has a finite number of elements, while a set or a [[multiset]] may have an infinite number of elements.