Are natural numbers the same as whole numbers, integers and rational numbers?

If not, which of these mean the same thing?


Natural numbers, whole numbers, integers and rational numbers?Are natural numbers the same as whole numbers, integers and rational numbers?
Natural numbers are not the same as whole numbers, because whole numbers include the number zero, while the natural numbers are ';counting'; numbers.





As a summary, here are the various sets of numbers:





Natural Numbers: { 1, 2, 3, 4, .... }


Whole Numbers: { 0, 1, 2, 3, 4, 5, .... }


Integers: { ... -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }


Rational Numbers: { All numbers of the form m/n, where m and n are both integers and n is non-zero}





All natural numbers are whole numbers (since the whole numbers are just the natural numbers, and includes zero).


All whole numbers are integers (since integers just open up the negative numbers)


All integers are rational numbers (since all integers can be expressed as themselves over 1, i.e. -5 is the same as -5/1, and 49 = 49/1).











Are natural numbers the same as whole numbers, integers and rational numbers?
Most books I've seen define the numbers like this...





natural numbers are 1, 2, 3, ...


whole numbers are 0, 1, 2, 3, ...


integers are -2, -1, 0, 1, 2, 3, ...


rational numbers are integers AND decimals like 3.2. They can't be decimals that go on forever without repeating like 3.4594382304... those are irrational numbers.








Hope this helps you! Please email for further clarification.