0
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.
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
Are the real numbers a borel set?
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.
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.
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.
Is intersection of two countably infinite sets can be finite?
Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.
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.
Are the real numbers a borel set?
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.
Is the intersection of the set of rational numbers and the set of whole numbers is the set of rational numbers?
No, it is not.
Are natural numbers the same of rational numbers?
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
Are integers in a set of rational numbers?
Yes - the set of integers is a subset of the set of rational numbers.
A set of numbers combining rational and irrational numbers?
The Real numbers
What is set of rational numbers union with integers?
It is the rational numbers.
Does a real number contain the set of rational numbers?
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.
How are rational numbers and integal numbers related to set of real numbers?
Both rational numbers and integers are subsets of the set of real numbers.
How are rational number different from fractional and whole number?
The set of rational numbers is the union of the set of fractional numbers and the set of whole numbers.
Is the set of rational numbers finite?
No; there are infinitely many rational numbers.
Is the set of rational numbers is larger than the set of integers?
Yes, rational numbers are larger than integer because integers are part of rational numbers.
