cofinal subset मीनिंग इन हिंदी

उदाहरण वाक्य

1. Partially ordered sets without greatest element or maximal elements admit disjoint cofinal subsets.
2. For example, the even and odd natural numbers form disjoint cofinal subsets of the set of all natural numbers.
3. Cofinal subsets are very important in the theory of directed sets and cofinal subnet is the appropriate generalization of  subsequence.
4. The cofinality of an ordinal \ alpha is the smallest ordinal \ delta that is the order type of a cofinal subset of \ alpha.
5. A more natural definition of a subnet would be to require " B " to be a cofinal subset of " A " and that " h " be the identity map.
6. They are also important in order theory, including the theory of cardinal numbers, where the minimum possible cardinality of a cofinal subset of " A " is referred to as the cofinality of " A ".
7. For a partially ordered set with maximal elements, every cofinal subset must contain all maximal elements, otherwise a maximal element which is not in the subset would fail to be " less than " any element of the subset, violating the definition of cofinal.