Natural numbers are the counting numbers: 1, 2, 3, 4, ...; some definitions also include 0 making the natural numbers the non-negative integers.
Irrational Numbers are those numbers which cannot be represented as a rational number, that is cannot be represented as a proper, or improper (top heavy), fraction with one integer over another. For example √2 and π are both irrational numbers whereas 1/2, 7/3 and 21 (= 21/1) are all rational 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.
Irrational numbers.
no it is not irrational irrational is a neverending number like2.36945856235......... that goes on and on 6 over 7 is a rational number rational numbers are whole numbers natural numbers and integers.
Irrational Numbers, Rational Numbers, Integers, Whole numbers, Natural numbers
Natural numbers or Counting numbers Integers Rational numbers Irrational numbers
All natural numbers are rational numbers. No irrational numbers are natural numbers.
No
No. All natural numbers are whole, so they are rational. Irrational numbers like pi and the square root of 34 come in decimals.
Cubes of all numbers are irrational numbers, if they're not natural
Quite the opposite. All natural numbers are rational. None of them are irrational.
No. Rather all natural numbers are necessarily rational number
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.
Irrational numbers.
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.
Irrational numbers have infinitely long, non-repeating decimal expansions. They cannot be natural numbers or whole numbers. Those are rational.
Irrational numbers are uncountably infinite. Although they can be ordered, they cannot be counted.
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.