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# pseudodifference

An element $z$ of lattice $L$ is *pseudodifference* of $y$ and $x$ ($y\setminus x$) if $z$ is the least element such that $y\leq x\cup z$.

*Pseudodifference* is denoted either as $\setminus$ or as $-$. Sometimes *pseudodifference* is denoted as $\setminus^{*}$.

The definition is borrowed from this online article.

Keywords:

difference,complement

Related:

Pseudocomplement,DifferenceOfLatticeElements

Synonym:

pseudo difference

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

06B99*no label found*

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## Comments

## An other formula for pseudodifference?

Pseudodifference of lattice L elements a and b is defined by the

formula:

a \* b = min { z in L | a <= (b /\ z) }.

Now one more formula:

a # b = \bigcup { x in L | x <= a and (x /\ b) = 0 }

(where 0 is the least lattice element).

Questions:

1. How "a # b" is called?

2. When a # b = a \* b?

--

Victor Porton - http://www.mathematics21.org

* Algebraic General Topology and Math Synthesis