0
Add your answer:
Earn +20 pts
What is the intersection between rational numbers and natural numbers?
It is the set of natural numbers.
What is the relation between integers natural numbers whole numbers rational and irrational numbers?
Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.
Is the square root of 81 rational?
Yes. The square root of 81 is 9 - a natural number and all natural numbers are rational numbers.
What are whole natural rational irrational numbers?
A while number can be expressed as itself over 1, eg 5 = 5/1; and this is one integer over another which is the form of rational numbers, so Whole numbers are rational numbers.
Which set of real numbers is bigger set of integers or set of rational numbers explain?
The question is not well-posed, in that the term "bigger" can be understood in different ways. If A is a subset of B, we can call B bigger than A. However, in set theory, the cardinality of a set is defined as the class of sets with the "same number" of elements: Two sets A and B have the same cardinality if there exists a bijection f:A->B. Theorem: If there is an injection i:A->B and an injection i:B->A, then there is a bijection f:A->B. Not proved here. The set of integers and the set of rational numbers can be mapped as follows. Since the natural numbers are a subset of the rational numbers by i:N->R: n-> n/1, we have half of the proof. Now, order the rational numbers as follows: - assign to each rational number p/q (p,q > 0) the point (p,q) in the plane. Next, consider that you can assign a natural number to each rational number by walking through them in diagonals: (1,1) -> 1; (2,1) -> 2; (1,2) -> 3; (3,1) ->4 ; (2,2) ->5; (1,3) -> 6; (4,1) -> 7; (3,2) -> 8, (2,3) -> 9; (1,4) -> 10, etc. (make a drawing). It is clear that in this way you can assign a unique natural number to EACH rational number. This means that you have an injection from the rational numbers to the natural numbers. Now you have two injections, from the natural numbers to the rational numbers and from the rational numbers to the natural numbers. By the theorem, there is a bijection, which means that the natural numbers and the rational numbers have the same cardinality. Neither of them is "bigger" than the other in this sense. The cardinality of these two sets is called Aleph-zero, and the sets are also called countable (because the elements can be counted with the 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.
Rational numbers are sometimes natural numbers?
Yes. All natural numbers are rational numbers.
What is a number that is a natural number and an irrational number?
Natural numbers are a part of rational numbers. All the natural numbers can be categorized in rational numbers like 1, 2,3 are also rational numbers.Irrational numbers are those numbers which are not rational and can be repeated as 0.3333333.
Give you a rational number that is a natural number?
All natural numbers are rational numbers.
Can a natural number be a rational number also?
All natural numbers are rational numbers.
A natural number is a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.
A natural number that is not a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.
What is a natural number that is not a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.
Are all rational numbers natural?
All of the natural numbers are rational, but there are still more rational numbers that aren't natural ones. Example: 1, 2, 3, 4, and 5 are all natural numbers, and they're all rational. 11/2, 21/2, 31/2, 41/2, and 51/2 are also rational, but they're not natural numbers.
What is the intersection between rational numbers and natural numbers?
It is the set of natural numbers.
A rational number that is also a natural number?
20 is both rational and natural. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Can a number be both rational and natural?
Yes. All natural numbers are rational.
