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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.
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What is the element of the intersection of the set of whole number and the set of natural numbers?
It is the set of natural numbers.
The set of whole numbers is equal to the set of natural numbers?
false, the set of natural numbers does not include 0, which can be considered a whole number.
What set of integers list the natural numbers?
Traditionally, the set of integers that represents the natural numbers is {1,2,3,...}, which are the positive integers. Some people include the non-negative integers as the set of natural numbers, which is {0,1,2,3,...}, and includes 0.
The set of whole numbers includes?
natural
What is the Set of natural numbers and zero?
0,1,2,3...
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.
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.
What numbers are in the set of natural numbers and which are in the set of whole numbers?
All of the natural numbers.
What is an example of a simple borel measurable function?
Characteristic function of any borel set is an example of simple Borel function
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 the element of the intersection of the set of whole number and the set of natural numbers?
It is the set of natural numbers.
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.
What is the intersection between rational numbers and natural numbers?
It is the set of natural numbers.
Another name for the set of natural numbers?
Another name for a set of natural numbers is counting numbers.
Does the set of whole numbers is larger than the set of natural numbers?
If you mean larger by "the set of whole numbers strictly contains the set of natural numbers", then yes, but if you mean "the set of whole numbers has a larger cardinality (size) than the set of natural numbers", then no, they have the same size.
The set of numbers that include the natural numbers their opposites and 0?
The set of numbers that include the natural numbers, their opposites and 0 is called the set of integers.
What is a set of numbers including zero and all the counting numbers?
Whole numbers are the set of natural or counting numbers inclding zero
