The formation of the concept of number. As early as primitive times, people noticed the difference in quantity between one sheep and many sheep, one wolf and the whole pack of wolves in production activities, and the concept of number gradually came into being with the passage of time.
Early counting system. At first, people counted with ten fingers. When fingers are not enough, people begin to count stones, knots and nicks.
Spring and Autumn Period and Warring States Period. During the Spring and Autumn Period and the Warring States Period, calculation has been widely used and decimal notation has been used, which is of epoch-making significance to the development of mathematics in the world.
Qin and Han dynasties. Qin and Han dynasties were the rising period of feudal society, with rapid economic and cultural development. It was during this period that the ancient mathematical system of China was formed. Its main symbol is that arithmetic has become a specialized subject and the emergence of mathematical works represented by Nine Chapters of Arithmetic.
Cardinality theory
Cardinality theory defines natural numbers as the cardinality of finite sets. This theory puts forward that two finite sets that can establish one-to-one correspondence between elements have the same quantitative characteristics, which are called cardinality. In this way, all the single element sets {x}, {y}, {a}, {b} and so on have the same cardinality, which is recorded as 1.
Similarly, whenever two fingers can establish a one-to-one set, their cardinality is the same, recorded as 2, and so on. The addition and multiplication of natural numbers can be defined by ordinal number or cardinal number theory, and the operations under the two theories are consistent.