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pseudodifference (Definition)

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

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

The definition is borrowed from this online article.




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"pseudodifference" is owned by porton.
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See Also: pseudocomplement, difference of lattice elements

Other names:  pseudo difference
Keywords:  difference, complement
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Cross-references: least element, lattice

This is version 2 of pseudodifference, born on 2008-04-06, modified 2008-04-06.
Object id is 10485, canonical name is Pseudodifference.
Accessed 715 times total.

Classification:
AMS MSC06B99 (Order, lattices, ordered algebraic structures :: Lattices :: Miscellaneous)

Pending Errata and Addenda
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An other formula for pseudodifference? by porton on 2009-07-15 18:59:13
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
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