maximal element वाक्य
उदाहरण वाक्य
मोबाइल
- This leaves open the possibility that there are many maximal elements.
- The infinite decimal numbers are the maximal elements within this order.
- A set can have several maximal elements without having a greatest element.
- Partially ordered sets without greatest element or maximal elements admit disjoint cofinal subsets.
- The existence of a maximal elements is proved via Zorn's lemma.
- Example 3 is an instance of existence of many maximal elements and no maximum.
- The Smith set is the maximal element of the beat-or-tie order.
- The converse is not true : there can be maximal elements despite there being no maximum.
- The set of maximal elements of a social preference is called the " core ".
- While this relation is not necessarily transitive, it does always contain at least one maximal element.
- If a poset has more than one maximal element, then these elements will not be mutually comparable.
- However, if it has a greatest element, it can't have any other maximal element.
- So, assume that P has at least one element, and let a be a maximal element of P.
- Zorn emigrated to the chain of subsets to have one chain not contained in any other, called the maximal element.
- In the second case the definition of maximal element requires m = s so we conclude that s \ leq m.
- Any least element or greatest element of a poset is unique, but a poset can have several minimal or maximal elements.
- That is, we should regard a rule as choosing the maximal elements ( " best " alternatives ) of some social preference.
- For totally ordered sets, the notions of maximal element and maximum coincide, and the notions of minimal element and minimum coincide.
- Every lower set L of a finite ordered set P is equal to the smallest lower set containing all maximal elements of L.
- An important tool to ensure the existence of maximal elements under certain conditions is "'Zorn's Lemma " '.
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