Two-dimensional arrays

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Index 2 refers to the third item, and index 6 refers to the seventh item. "2" is nominal (name) while "third" is ordinal (position).

Here's one way I like to visualize index numbers:

  _________________
  |   |   |   |   |
  | A | B | C | D |
  |___|___|___|___|
  0   1   2   3   4
  ^
  |
index

Imagine an array is like a ruler. A ruler starts at 0, just as index numbers do. An index (e.g., 0) refers to the entire "unit" up to but not including the next index (e.g., 1). The size of this array is 4, which means indexes can go up to but not including 4.

Understanding the "up to but not including" concept is very useful in a lot of different areas of computer science—time, for example (a day starts at 0 and goes up to but not including 86400 seconds (discounting days with leap seconds)).

See also E.W. Dijkstra Archive: Why numbering should start at zero (EWD 831).