countable set sentence in Hindi
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- It is consistent with ZF that \ omega _ 1 be the limit of a countable sequence of countable ordinals as well as the set of real numbers is countable union of countable sets.
- An easy proof notes that x is the union of y and x \ y, and the union of two countable sets is countable, so one of the two must be uncountable.
- This then opens the question as to what sort of set to a countable set, such as " f " and " g " above, can actually be constructed.
- A necessary condition for this to be the case is that there is a countable set of " H " invariant Borel sets which separate the orbits of " H ".
- This set is the union of the length-1 sequences, the length-2 sequences, the length-3 sequences, each of which is a countable set ( finite Cartesian product ).
- Note that the underlying index set can be taken to be any countable set ( and in fact any set whatsoever, provided is defined appropriately, as is explained in the article Hilbert space ).
- However in this case the class of all constructible sets plays the same role as the minimal model and has similar properties ( though it is now a proper class rather than a countable set ).
- W in V that is a minimal model "'of ZFC . Using the downward L�wenheim Skolem theorem, one can show that the minimal model ( if it exists ) is a countable set.
- I don't know whether you can prove in ZFC alone that there exists a largest countable set in any of these pointclasses .-- talk ) 23 : 14, 27 December 2009 ( UTC)
- We cannot eliminate the Hausdorff condition; a countable set with the indiscrete topology is compact, has more than one point, and satisfies the property that no one point sets are open, but is not uncountable.
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