Ordered Lists

If we consider "the songs on my iPod" as a familiar example of a set, then "a playlist on my iPod" is the corresponding example of an ordered list. Key properties of ordered lists include:

  • Order of elements in an ordered list is relevant.
  • Repetition of elements in an ordered list is relevant.

Explicit notion for writing ordered lists is similar to that for sets; however, we use parentheses instead of curly braces. For example:

  • (1,2) is an ordered list that is different than (2,1)
  • (1,1) is an ordered list that is different than (1)

From now on, expressions with parentheses "( , , , )" and expressions with curly braces "{ , , , }" have very distinct meanings!

The length of an ordered list is, intuitively speaking, just like the number of songs in a playlist. For example:

  • The length of (1,10) is 2
  • The length of (1,1,2,2) is 4

An ordered pair is an ordered list of length two. We will use ordered pairs very often in our study of the Web; we will use longer ordered lists less often. Also, we will never attempt to define the cardinality of an ordered list. Sets have cardinality. Ordered lists have length.

Any element in an ordered list can itself be an ordered list or a set. Any object in a set can be a set or an ordered list. For example:

  • {(1,2),(3,4)} is a set of two elements, each of which is an ordered pair. One of the elements of the set is (1,2) and the other element of the set is (3,4).
  • ({1,2},{3},{2,4}) is an ordered list of sets. The first element of the list is the set {1,2}; the second element of the list is the set {3}; the third element of the list is the set {2,4}.
 
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