The basic definition of product in elementary arithmetic is the number or quantity obtained by multiplying two or more numbers or quantities. Sometimes called products. The concept of product depends on the definition of "multiplication". When people upgrade the set of multiplication objects to more general sets, such as groups, rings, fields, etc. The concept of the product will also change.
Multiplication is a shortcut to add up the same numbers. The result of its operation is called product, and "X" is the symbol of multiplication. From the philosophical point of view, multiplication is the result of qualitative change caused by additive quantity. The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is a systematic summary of this basic definition. Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value. Integer multiplication meets the following requirements: exchange law, association law, distribution law and elimination law.
Multiplicative commutative law is a calculation rule. When two numbers are multiplied, the position of the exchange factor remains unchanged, and their product is called multiplication exchange law, which is expressed by the formula: A× B = B× A. When three numbers are multiplied, the positions of the two factors can be exchanged at will, and the product remains unchanged, which is expressed by the formula: A× B× C = B× A× C = A× C× B.
Multiplicative associative law is a kind of multiplication operation. When three numbers are multiplied, multiply the first two numbers and then another number, or multiply the last two numbers and then another number, and the product remains the same. This is called the law of multiplication and association. Expressed by the formula: (a×b)×c=a×(b×c).