dense set वाक्य
उदाहरण वाक्य
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- The elements of the van der Corput sequence ( in any base ) form a dense set in the unit interval; that is, for any real number in [ 0, 1 ], there exists a subsequence of the van der Corput sequence that converges to that number.
- However it is the intersection of countably many open dense sets, and thus comeager-- the set of all sequences that has some polynomial with a root in a given basic open neighborhood is open dense .-- talk ) 08 : 32, 10 April 2008 ( UTC)
- One of Baumgartner's results is the consistency of the statement that any two \ aleph _ 1-dense sets of reals are order isomorphic ( a set of reals is \ aleph _ 1-dense if it has exactly \ aleph _ 1 points in every open interval ).
- In his 1975 short story " The Book of Sand " ( " El Libro de Arena " ), he deals with another form of infinity; one whose elements are a dense set, that is, for any two elements, we can always find another between them.
- After committing the embarassing rookie's mistake of linking the phrase " dense in itself " in the sentence " a nowhere dense set is always dense in itself " to dense-in-itself I got myself thinking : why is the notion of a set being dense-in-itself at all useful?
- Since you have already defined it on a dense set, you can extend the function to the unique continuous extension, but now you need to prove that all the derivatives exist at these new points and that the derivatives are eventually 0 .-- talk ) 07 : 41, 16 November 2010 ( UTC)
- Every subset of a nowhere dense set is nowhere dense, and the countably many nowhere dense sets, however, need not be nowhere dense . ( Thus, the nowhere dense sets need not form a sigma-ideal . ) Instead, such a union is called a " meagre set " or a " set of first category ".
- Every subset of a nowhere dense set is nowhere dense, and the countably many nowhere dense sets, however, need not be nowhere dense . ( Thus, the nowhere dense sets need not form a sigma-ideal . ) Instead, such a union is called a " meagre set " or a " set of first category ".
- Every subset of a nowhere dense set is nowhere dense, and the countably many nowhere dense sets, however, need not be nowhere dense . ( Thus, the nowhere dense sets need not form a sigma-ideal . ) Instead, such a union is called a " meagre set " or a " set of first category ".
- Of fundamental importance is the following theorem of Hausdorff : for each unbounded ordered dense set A there are two uniquely determined regular initial numbers \ omega _ { \ xi }, \ omega _ { \ eta } so that A is cofinal with \ omega _ { \ xi } and coinitial with \ omega _ { \ eta } ^ * ( * Denotes the inverse order ).
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