Review Note
Last Update: 11/12/2024 10:01 PM
Current Deck: ETH CS::Discrete Math
Published
Fields:
Front
Special elements in posets (minimal, least, lower bound, greatest lower bound)
Back
Official definition:
For simplicity you can also define a minimal element as an element, s.t. no other element is related to it.
Similarly, a maximal element is an element could be defined as an element, s.t. it is related to no other element.
A least element contrary however, must be related to every other element. (for example 1 is the least element in the divides relation on the natural numbers)
Upper and lower bounds:
A least upper bound and greatest lower bound:
For simplicity you can also define a minimal element as an element, s.t. no other element is related to it.
Similarly, a maximal element is an element could be defined as an element, s.t. it is related to no other element.
A least element contrary however, must be related to every other element. (for example 1 is the least element in the divides relation on the natural numbers)
Upper and lower bounds:
A least upper bound and greatest lower bound:
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