difference of lattice elements
Let . A of and is an element that and . When there is only one difference of and , it is denoted .
One immediate property is: is the unique difference of any element and itself (). For if is such a difference, then and . So by the second equation, and hence that by the first equation.
For arbitrary lattices of two given elements do not necessarily exist. For some lattices there may be more than one difference of two given elements.
For a distributive lattice with bottom element , the difference of two elements, if it exists, must be unique. To see this, let and be two differences of and . Then
So . Similarly, . As a result, .
|Title||difference of lattice elements|
|Date of creation||2013-03-22 17:57:44|
|Last modified on||2013-03-22 17:57:44|
|Last modified by||porton (9363)|