least element वाक्य
उदाहरण वाक्य
मोबाइल
- Similar conclusions hold for least elements.
- Complete lattices and orders with a least element ( the " empty supremum " ) provide further examples.
- Every recursively enumerable ( or even hyperarithmetic ) nonempty subset of this total ordering has a least element.
- Equivalently, one may define an atom to be an element that is covers the least element "'0 " '.
- As defined in set theory, the maximum and minimum of a greatest and least elements in the set, respectively.
- Dcpos with a least element ( " pointed dcpos " ) are called complete partial order ( cpo ).
- The College Logo combines the Logos of St . Brendan s and Shaw Colleges, or at least elements from each.
- By definition, this is the least element among all elements that are greater than each member of the empty set.
- By the above reasoning the map exists and is unique since least elements of subsets of wellordered sets are unique.
- In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology.
- Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.
- The main property to derive this uniqueness is the following : For every in, is the least element of such that.
- Any least element or greatest element of a poset is unique, but a poset can have several minimal or maximal elements.
- One can define half-closed and closed intervals,, and by adjoining as a least element and / or as a greatest element.
- By using e " instead of d " in the above definition, one defines the least element of " S ".
- It is easy to see that 0 is the least element with respect to this order : for all " a ".
- Here's the general proof : suppose " X " is a nonempty set that you wish to prove has a least element.
- An example is given by the above divisibility order |, where 1 is the least element since it divides all other numbers.
- The greatest element in this fiber is the discrete topology on " X " while the least element is the indiscrete topology.
- An important property of the natural numbers is that they are well-ordered : every non-empty set of natural numbers has a least element.
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