Essential Ideas for Section 3.1

A number is used to answer the question "How many?" and usually refers to numbers used to count objects:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}

This set of numbers is called the set of counting numbers. A numeral is a symbol used to represent a number, and a numeration system consists of a set of basic symbols and some rules for making other symbols from them, the purpose being the identification of all numbers.