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Is natural and rational numbers the same thing?

Updated: 8/20/2019
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Yes.

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Q: Is natural and rational numbers the same thing?
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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.


Why are natural numbers rational numbers?

Natural numbers are a special kind of Rational numbers. Rational numbers can be expressed as a fraction. (Positive) fractions with the same (nonzero) numerator and denominator are natural numbers, for example 9/9 = 1.


How can you represent how sets of a whole numbers integers and rational numbers are related to each other?

Whole numbers and integers are the same thing. They are a proper subset of rational 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.


What coefficients can you use in polynomials?

Any. They can be integers, rational numbers (the same thing if you multiply out by their LCM), real numbers or even complex numbers.


What does whole number rational number and integer mean?

Whole number means the same thing as integer and does not have a fraction or decimal part. Rational numbers can be expressed as a ratio of whole numbers.


What is the same about rational and irrational numbers?

it has the word rational in it


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 rational numbers the same as whole numbers?

No, they are not.


Are there more rational number than irrational numbers?

There are more irrational numbers than rational numbers. The rationals are countably infinite; the irrationals are uncountably infinite. Uncountably infinite means that the set of irrational numbers has a cardinality known as the "cardinality of the continuum," which is strictly greater than the cardinality of the set of natural numbers which is countably infinite. The set of rational numbers has the same cardinality as the set of natural numbers, so there are more irrationals than rationals.


How are whole numbersintegers and rational numbers related?

Whole numbers and integers are the same. They are a proper subset of rational numbers.


How are integers and rational numbers the same?

Because both can be expressed as fractions