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.