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# What are rational whole. irrational and natural numbers?

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## Related Questions

###### Asked in Math and Arithmetic, Numbers , Irrational 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.

###### Asked in Math and Arithmetic, Numbers

### Is the number 56 a rational number whole number natural number or irrational number?

56 is a rational whole natural number.
Or to put it another way:
56 is a Natural number, but as all natural numbers are also
whole numbers 56 is also a whole number, but as all whole numbers
are also rational numbers 56 is also a rational number.
Natural numbers are a [proper] subset of whole numbers;
Whole numbers are a [proper] subset of rational numbers.
The set of rational numbers along with the set of irrational
numbers make up the set of real numbers