Misc math articles and essays

This page contain my misc math articles and essays not fitting to other categories on my math site.

Vertical order of binary relations

Defined a partial order relation between binary relations f and g by the formula g = f|_{dom g}.

Theorem (with proof), expanding and generalizing the following statement:

For two binary relations f and g the formula g = f|_{dom g} is equivalent to conjunction of g being a subset of f and the formula

g g^-1 = f g^-1 (or equivalently g g^-1 = g f^-1).