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All integers are rational numbers, not all rational numbers are integers. Rational numbers can be expressed as fractions, p/q, where q is not equal to zero. For integers the denominator is 1.

5 is an integer, 2/3 is a fraction, both are rational.

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Integers consist of natural numbers(1, 2, 3,...), zero and the negative natural numbers(-1, -2, -3,...). 1, 2, 3 etc are positive integers and -1, 2, -3 etc are negative integers. Whereas rational numbers consist of integers as well as numbers in the form of p/q where p and q are integers and q is not equal to zero.

So the main difference formed is:-

Every integer is a rational number but every rational number is not an integer.

Rational numbers can be written as a fraction integers include both positive and negative numbers.

All integers are rational numbers, not all rational numbers are integers.

An integer, in its simplest form as a rational number, must have a denominator of 1.

Q: How are integers and rationals numbers different?

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Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.

Natural (or counting) numbers Integers Rationals Irrationals Transcendentals

There are an infinite number of subsets: All rationals other than 1 All rationals other than 2, etc All rationals other than 1.1 All rationals other than 2.1, etc, etc. All integers

The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.

Since rational numbers are expressed as a/b where a & b are integers, in a sense fractions & rationals means the same thing. Integers may be considered fractions with denominators of 1 or other improper fractions. In any case, most real numbers are irrational; the rationals are just one type of real number.

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Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.

Negative integers, rationals and real numbers

Integers, rationals, reals, complex numbers, etc.

Natural (or counting) numbers Integers Rationals Irrationals Transcendentals

no, a rational number can also be a fraction or decimal

Integers, rationals. Also all subsets of these sets eg all even numbers, all integers divided by 3.

Yes. There is an injective function from rational numbers to positive rational numbers*. Every positive rational number can be written in lowest terms as a/b, so there is an injective function from positive rationals to pairs of positive integers. The function f(a,b) = a^2 + 2ab + b^2 + a + 3b maps maps every pair of positive integers (a,b) to a unique integer. So there is an injective function from rationals to integers. Since every integer is rational, the identity function is an injective function from integers to rationals. Then By the Cantor-Schroder-Bernstein theorem, there is a bijective function from rationals to integers, so the rationals are countably infinite. *This is left as an exercise for the reader.

-28 belongs to: Integers, which is a subset of rationals, which is a subset of reals, which is a subset of complex numbers.

Negative integers, integers, negative rationals, rationals, negative reals, reals, complex numbers are some sets with specific names. There are lots more test without specific names to which -10 belongs.

There are an infinite number of subsets: All rationals other than 1 All rationals other than 2, etc All rationals other than 1.1 All rationals other than 2.1, etc, etc. All integers

Yes. Rational numbers are numbers that can be written as a fraction. All rationals are real.

The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.