Why aren't positive rational numbers considered "natural numbers?"

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Andrew_Stephenson

A positive rational number is defined as the ratio of 2 natural numbers.

So why should positive rational numbers by defined natural numbers as well, when they the product of nothing but natural numbers?

Gomer_Pyle

Natural numbers are numbers you can count on your fingers and toes (if you had enough of them). There are no partial numbers or fractions. Some people start the natural numbers at 0. Others say they must be counting numbers and start at 1. All rationals can be described as the the ratio of two naturals. I'm not sure if rational numbers that also equate to a natural number (like 6/2=3) are still considered rational or just natural.

Some numbers like pi are neither natural nor rational. It is certainly not a counting number and it can't be defined by any known ratio of naturals.

mantine73

Natural numbers start at 0 and integers at 1

Andrew_Stephenson

Whole Numbers start at 0, while Natural Numbers start 1. It is not fully agreed upon, in academia, if "Counting Numbers" should be second or first name for the Wholes or Naturals.