What is the complement of a countable set?

What is the complement of a countable set?

In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many elements of X. While the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals.

How will we describe a countable set?

In mathematics, a set is countable if it has the same cardinality (the number of elements of the set) as some subset of the set of natural numbers N = {0, 1, 2, 3.}. A countable set is either a finite set or a countably infinite set.

What is complement of a finite set?

In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set. In other words, A contains all but finitely many elements of X. If the complement is not finite, but it is countable, then one says the set is cocountable.

Is the complement of a countable set uncountable?

The set of non-negative numbers is uncountable, and its complement in R, the set of negative numbers, is also uncountable.

Is the complement of a countable set countable?

Yes. For any two sets and , if then . If is a countable set, then so is . It can be a finite or infinite set; either way it is countable.

Is the complement of an uncountable set countable?

What is the meaning of complement of a set?

In set theory, the complement of a set A, often denoted by Ac (or A′), are the elements not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U that are not in A.

What is meant by countable noun?

Countable nouns are for things we can count using numbers. They have a singular and a plural form. The singular form can use the determiner “a” or “an”. If you want to ask about the quantity of a countable noun, you ask “How many?” combined with the plural countable noun. Singular.