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If we scan along the ''X'' dimension we see that the "''Y'' incidence degrees" of the ''X'' nodes 0 through 9 are 0, 1, 2, 3, 1, 1, 1, 2, 0, 0, in order.

If we scan along the <math>~X~</math> dimension from <math>~0~</math> to <math>~9~</math> we see that the incidence degrees of the <math>~X~</math> nodes with the <math>~Y~</math> domain are <math>~0, 1, 2, 3, 1, 1, 1, 2, 0, 0,~</math> in that order.

If we scan along the ''Y'' dimension we see that the "''X'' incidence degrees" of the Y nodes 0 through 9 are 0, 0, 3, 2, 1, 1, 2, 1, 1, 0, in order.

If we scan along the <math>~Y~</math> dimension from <math>~0~</math> to <math>~9~</math> we see that the incidence degrees of the <math>~Y~</math> nodes with the <math>~X~</math> domain are <math>~0, 0, 3, 2, 1, 1, 2, 1, 1, 0,~</math> in that order.

Thus, ''E'' is not total at either ''X'' or ''Y'', since there are nodes in both ''X'' and ''Y'' having incidence degrees that equal 0.

Thus, <math>~E~</math> is not total at either <math>~X~</math> or <math>~Y,~</math> since there are nodes in both <math>~X~</math> and <math>~Y~</math> having incidence degrees less than 1.

Also, ''E'' is not tubular at either ''X'' or ''Y'', since there exist nodes in both ''X'' and ''Y'' having incidence degrees greater than 1.

Also, <math>~E~</math> is not tubular at either <math>~X~</math> or <math>~Y,~</math> since there are nodes in both <math>~X~</math> and <math>~Y~</math> having incidence degrees greater than 1.

Clearly, then, ''E'' cannot qualify as a pre-function or a function on either of its relational domains.

Clearly, then, <math>~E~</math> cannot qualify as either a pre-function or a function on either of its relational domains.

===Commentary Note 11.6===

===Commentary Note 11.6===