0
all finite set is countable.but,countable can be finite or infinite
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
What are the different types a of set?
A null set, a finite set, a countable infinite set and an uncountably infinite set.
What is the difference between a finite set and an infinite set?
Set A is a finite set if n(A) =0 (that is, A is the empty set) or n(A) is a natural number. A set whose cardinality is not 0 or a natural number is called an infinite set.
What is countable set and uncountable set?
A countable set is defined as one whose elements can be put into one-to-one correspondence with elements of the set of counting numbers or some subset of it. A countable set can be infinite: for example all even numbers. This raises the strange concept where a subset (positive even numbers) has the same cardinality as all counting numbers - which should be a set that is twice as large! Even more confusingly (perhaps) is the fact that the set of all rational numbers also has the same cardinality as the set of counting numbers. You need to go to the set of irrationals or bigger before you get to uncountable sets. So you have the weird situation in which there are more irrationals between 0 and 1 than there are rationals between from 0 and infinity (if infinity can be treated as a value)! There is a minority definition of countable which means containing a finite number of elements as opposed to uncountable meaning infinitely many elements. However, these definitions are essentially the same as the finite sets and infinite sets and so there is little point in using them.
Is a set of prime numbers an finite set?
Finite, no.
Why is an empty set a finite set?
An empty set is considered a finite set because it contains zero (0) elements and zero is a finite number.
What are the different types a of set?
A null set, a finite set, a countable infinite set and an uncountably infinite set.
What is the difference between a finite set and an infinite set?
Set A is a finite set if n(A) =0 (that is, A is the empty set) or n(A) is a natural number. A set whose cardinality is not 0 or a natural number is called an infinite set.
What the differentiate between finite set and infinite set?
A finite set has a finite number of elements, an infinite set has infinitely many.
Is counting measure indeed a measure and is this always sigma-finite?
It is a measure, but it isn't always sigma-finite. Take your space X = [0,1], and u = counting measure if u(E) < infinity, then E is a finite set, but there is no way to cover the uncountable set [0,1] by a countable collection of finite sets.
What is countable set and uncountable set?
A countable set is defined as one whose elements can be put into one-to-one correspondence with elements of the set of counting numbers or some subset of it. A countable set can be infinite: for example all even numbers. This raises the strange concept where a subset (positive even numbers) has the same cardinality as all counting numbers - which should be a set that is twice as large! Even more confusingly (perhaps) is the fact that the set of all rational numbers also has the same cardinality as the set of counting numbers. You need to go to the set of irrationals or bigger before you get to uncountable sets. So you have the weird situation in which there are more irrationals between 0 and 1 than there are rationals between from 0 and infinity (if infinity can be treated as a value)! There is a minority definition of countable which means containing a finite number of elements as opposed to uncountable meaning infinitely many elements. However, these definitions are essentially the same as the finite sets and infinite sets and so there is little point in using them.
Is every subset of a finite set is a finite?
prove that every subset of a finite set is a finite 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.
Is every subset of a countable set is countable?
Yes.
Is a set of prime numbers an finite set?
Finite, no.
What is countable infinite population?
A countable set has elements (or members) that can be listed, like the numbers 1, 2, 3, and so on. You must be able to associate each element with a natural number. The interval of all the real numbers between 0 and 1, is not countable. But the interval of all rational numbers between 0 and 1 is countable. We could list the first element as 0, the second element as 1, the third element as 1/2, the fourth as 1/4, the fifth as 3/4, the sixth as 1/3, the seventh as 2/3, and so on. This set is also infinite because there is no finite bound on the number of elements. The term "population" has many meanings. A "countable infinite population" probably refers to a statistical population. This is a particular kind of set considered by statistics.
What are the examples of a finite set?
In mathematics, a finite set is a set that has a finite number of elements. For example, (2,4,6,8,10) is a finite set with five elements. The number of elements of a finite set is a natural number (non-negative integer), and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: (1,2,3,4, . . .)
Is the set of all irrational number countable?
No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)
