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no, a rational number can also be a fraction or decimal
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Which subsets of numbers cannot be irrational?
Integers, rationals. Also all subsets of these sets eg all even numbers, all integers divided by 3.
What are subsets of rational numbers?
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
Are all real numbers a rational numbers?
Yes. Rational numbers are numbers that can be written as a fraction. All rationals are real.
-30 belongs to what family of the real numbers?
Negative integers, rationals and real numbers
What set of numbers does -23 belong to?
Integers, rationals, reals, complex numbers, etc.
What are the hierarchy of real numbers?
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.
What represents fractions?
Q represents the set of all rational numbers, Zrepresents the set of all integers so Q excluding Z, represents all rationals that are not integers.
Diff kind of real numbers?
Natural (or counting) numbers Integers Rationals Irrationals Transcendentals
The number -4 is what set of numbers?
The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.
What is the set of all numbers containing zero as well as all postitive and negative numbers?
The answer depends on what do you mean by "all". It could be the set of all integers, the set of all rationals or the set of all reals.
Is the cardinality of an infinitely countable set the same as the rational numbers?
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.
What are all the numbers that are not prime or composite?
The property of prime or composite applies only to integers. All other numbers (non-integer rationals and all irrational numbers) are neither prime nor composite. Within integers, 0 and 1 are neither prime nor composite.
