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# What is the order from largest to smallest for whole number integers rational numbers natural number irrational numbers and real numbers?

Wiki User

2012-09-17 20:47:40

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.

Wiki User

2012-09-17 20:47:40
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