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No. Although there are infinitely many of either, there are more Irrational Numbers than rational numbers.
The cardinality of the set of rational numbers is À0 (Aleph-null) while the cardinality of the set of irrational numbers is 2À0.
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Can a real number that is not a rational number be an irrational number?
Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.
Set and the different of sets?
there are 5 diffeerent sets Natural Numbers whole numbers integers rational numbers irrational numbers.
What is the set of numbers made of rational numbers and irrational numbers?
These two sets together make up the set of real numbers.
What is the order from largest to smallest for whole number integers rational numbers natural number irrational numbers and real numbers?
Such numbers cannot be ordered in the manner suggested by the question because: For every whole number there are integers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every integer there are whole numbers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every rational number there are whole numbers, integers, natural numbers, irrational numbers and real numbers that are bigger. For every natural number there are whole numbers, integers, rational numbers, irrational numbers and real numbers that are bigger. For every irrational number there are whole numbers, integers, rational numbers, natural numbers and real numbers that are bigger. For every real number there are whole numbers, integers, rational numbers, natural numbers and irrational numbers that are bigger. Each of these kinds of numbers form an infinite sets but the size of the sets is not the same. Georg Cantor showed that the cardinality of whole numbers, integers, rational numbers and natural number is the same order of infinity: aleph-null. The cardinality of irrational numbers and real number is a bigger order of infinity: aleph-one.
Why 2 set are irrational and rational are separate?
Because irrational numbers are defined as those that are not rational. The dichotomy means that every real number belongs to one or the other of these sets, and never to both.
