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

 Pointfree binary relations

I define pointfree binary relations, a way to describe binary
relations and more general structures without referring to particular
"points" (elements).
 Logics

 Formalistics of generalization

In the framework of ZF formally considered generalizations, such as whole
numbers generalizing natural number, rational numbers generalizing whole
numbers, real numbers generalizing rational numbers, complex numbers
generalizing real numbers, etc. The formal consideration of this may be
especially useful for computer proof assistants.
 Vertical order of binary relations

 Vertical order of binary relations

Defined a partial order relation between binary relations
f and g by the formula
g = f_{dom g}.
 Theorem about binary relation limited to a set
(WARNING: This theorem appeared to be erroneous.)

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}).
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