Definition:Lexicographic Order/Ordinals

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Definition

The lexicographic order is a relation on ordered pairs of ordinals denoted $\preccurlyeq_l$.

$\preccurlyeq_l$ is the set of all ordered pairs $\tuple {\tuple {\alpha, \beta}, \tuple {\gamma, \delta} }$ such that:

$(1): \quad$ Each $\alpha, \beta, \gamma, \delta$ is a member of the class of all ordinals
$(2): \quad$ $\alpha \in \gamma$ or $\alpha = \gamma \land \beta \in \delta$


Also known as

Lexicographic order can also be referred to as the more unwieldy lexicographical ordering.

Some sources refer to it as dictionary order.

Some sources classify the lexicographic order as a variety of order product.

Hence the term lexicographic product can occasionally be seen.


The mathematical world is crying out for a less unwieldy term to use.

Some sources suggest Lex, but this has yet to filter through to general usage.


Also see

  • Results about the lexicographic order can be found here.


Sources