This is the set of numbers^{1} :

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 *arithmetic*^{2} . 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 numbers*^{3} . For
example:

(2) |

or

(3) |

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