What is lexicographical order?

Alphabetical order is a specific kind of lexicographical ordering. The term lexicographical often refers to the mathematical rules or sorting. These include, for example, proving logically that sorting is possible. Read more about lexicographical order on wikipedia

Alphabetical ordering includes variants that differ in how to handle spaces, uppercase characters, numerals, and punctuation. Purists believe that allowing characters other than a-z makes the sort not "alphabetic" and therefore it must fall in to the larger class of "lexicographic". Again, wikipedia has additional details.

In computer programming, a related question is dictionary order or ascii code order. In dictionary order, the uppercase "A" sorts adjacent to lowercase "a". However, in many computer languages, the default string compare will use ascii codes. With ascii, all uppercase letters come before any lowercase letters, which means that that "Z" will sort before "a". This is sometimes called ASCIIbetical order.

lexicographical order is alphabetical order. The other type is numerical ordering. Consider the following values,

1, 10, 2

Those values are in lexicographical order. 10 comes after 2 in numerical order, but 10 comes before 2 in "alphabetical" order.