The consistency of number recognition and operation refers to the consistency of basic concepts and operation rules in mathematics in different fields and applications. Mainly reflected in the following aspects: the expansion of natural numbers, the expansion of natural numbers, the reversibility of operation, the consistency of relational symbols and the consistency of operation results.

Expansion of natural numbers: the understanding of logarithm begins with natural numbers and gradually extends to the fields of integers, rational numbers, real numbers and complex numbers. Numbers in different number fields have similar properties and operation rules, and maintain consistency. Continuation of arithmetic rules: the applicability of arithmetic rules and properties in different number fields is consistent. For example, addition and multiplication satisfy commutative law, associative law and distributive law, which are all valid in the fields of natural numbers, integers, rational numbers and real numbers.

Reversibility of operation: Reversibility of operation refers to the common inverse operation in mathematics. For example, the inverse operation of addition is subtraction and the inverse operation of multiplication is division. These inverse operations have the same effect in different number fields. Consistency of relational symbols: common relational symbols in mathematics (such as "=", "

Consistency of operation results: For the same mathematical operation, whether in simple integer operation or in more complex mathematical fields such as linear algebra, the laws and properties of operation results are consistent. These consistency principles enable mathematics to reason and operate in different fields, and ensure the logic and reliability of mathematics. They form the foundation of the mathematical system and provide a solid foundation for the application and development of mathematics.

The concept of numbers

Counting demand: human beings need to count and record the number in daily life, such as counting the number of livestock and calculating grain reserves. Through statistics, people can better manage resources and communicate.

Natural observation: By observing the phenomena in nature, people have discovered some laws and quantitative relations. For example, it is found that the hand index corresponds to the number 1~ 10, and the change of the moon's round and round corresponds to a month's time.