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## definition

An ordinal ruler has these features:

• It has line (segments).
• It is graduated with ordinals.
• The ordinals are in order. Smaller ones in the left and larger ones in the right.

(note that an ordinary ruler is an ordinal ruler)

## how to make an ordinal ruler

There are many ways to make one, so I will write one of the simple ways.

• First, write two ordinals at the ends. By the definition, the left one must be smaller.
• For every line segment between $\alpha$ and $\beta$,
• If $\beta=\alpha+1$, write nothing between.
• If $\alpha$ is included in the fundamental sequence of $\beta$, write the next term of the fundamental sequence at halfway between them.
• Else, write the smallest term of the fundamental sequence of $\beta$ which is bigger than $\alpha$.

(note that the graduations can be infinitely many)

## examples

The image is two of the ordinals made by above recipe.

## use

You may be able to use it for googology graph.