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# Natural, or Counting Numbers

This is the set of numbers1 :

that is pretty much the first piece of mathematics any student learns. They are used to count, initially to count things, concrete objects such as pennies or marbles. This is in some respects surprising, since pennies and marbles are never really identical. In physics, however, one encounters particles that are - electrons, for example, differ only in their position or orientation.

The natural numbers are usually defined along with a set of operations known as arithmetic2 . The well-known operations of arithmetic are addition, subtraction, multiplication, and division. One rapidly sees that the set of natural/counting numbers is not closed with respect to them. That just means that if one subtracts 7 from 5, one does not get a natural number; one cannot take seven cows away from a field containing five cows, one cannot remove seven pennies from a row of five pennies.

Natural numbers greater than 1 in general can be factored into a representation in prime numbers3 . For example:

 (2)

or

 (3)

This sort of factorization can sometimes be very useful, but not so much in introductory physics.

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Robert G. Brown 2011-04-19