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Yes, since the set of real numbers can be expressed as a countable union of closed sets.
In fact if we're talking about subsets of the real numbers (R), then by definition R is in all sigma-algebras of R including the Borel sigma-algebra, and so is a Borel set.
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Can set of rational numbers forms a borel set?
Yes. the set of rational numbers is a countable set which can be generated from repeatedly taking countable union, countable intersection and countable complement, etc. Therefore, it is a Borel Set.
Give an example of a subset of R that is not a Borel set?
An example is given here: http://en.wikipedia.org/wiki/Non-Borel_set Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated. Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set. See http://en.wikipedia.org/wiki/Non-measurable_set = =
What is example of subset in math?
The set of Rational Numbers is a [proper] subset of Real Numbers.
According to the ruler postulate what does the set of points on any line correspond to?
Real numbers
What a equal sets?
What are equal sets?? A set is a grouping of numbers. Set P = {1,4,9} if set Q is equal it must contain exactly the same numbers.
Are the natural numbers a Borel set?
A singleton point is a closed set. The natural numbers can be written as a countable union of points. Thus, they form a Borel set.
Can set of rational numbers forms a borel set?
Yes. the set of rational numbers is a countable set which can be generated from repeatedly taking countable union, countable intersection and countable complement, etc. Therefore, it is a Borel Set.
What is an example of a simple borel measurable function?
One example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.
What has the author Pierre-Arnold Borel written?
Pierre-Arnold Borel was a French mathematician known for his work in set theory and real analysis. He is best known for his contributions to measure theory and the Borel algebra.
What is the set of numbers including all irrational and rational numbers?
real numbers
Give an example of a subset of R that is not a Borel set?
An example is given here: http://en.wikipedia.org/wiki/Non-Borel_set Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated. Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set. See http://en.wikipedia.org/wiki/Non-measurable_set = =
What is A set of numbers that is larger than the set of real numbers?
In a certain sense, the set of complex numbers is "larger" than the set of real numbers, since the set of real numbers is a proper subset of it.
What is the set of numbers that includes all rational and all irrational numbers?
the set of real numbers
Derived Set of a set of Rational Numbers?
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
The set of all rational and irrational numbers?
Are disjoint and complementary subsets of the set of real numbers.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
What is the difference between a set of real numbers and a set of complex numbers?
The set of real numbers is a subset of the set of complex numbers. For the set of complex numbers, given in the form (a + bi), where a and b can be any real number, the number is only a real number, if b = 0.
