## 4.1 Outline

- Basic ideas
- number
- counting number
- numeral
- numeration system

- Egyptian numeration system
- simple grouping system
- hieroglyphic symbols
- addition principle
- repetitive system

- Roman numeration system
- Roman numerals
- subtractive principle
- multiplicative principle

- Babylonian numeration system
- positional system
- cuneiform symbols
- properties of numeration systems
- definition
- simple grouping system
- positional system
- addition principle
- subtraction principle
- repetitive system

- Other historical systems
- decimal
- Greek
- Mayan
- Chinese

## 4.1 Essential Ideas

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.