2. The formula of multiplicative associative law: (a×b)×c=a×(b×c)
3. Multiplicative commutative law formula: a× b = b× a.
4. The formula of additive associative law: (a+b)+c=a+(b+c)
The multiplication of integers satisfies:? Reduction of criminal law, combination method, distribution method, elimination method. With the development of mathematics, the object of operation has developed from integer to more general group. Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous example of noncommutativity was discovered by Hamilton? Quaternion group. But the law of association is still satisfied.
Multiply three numbers, the first two numbers are multiplied and then multiplied, or the last two numbers are multiplied and then multiplied, and the product remains the same.
The main formula is a×b×c=a×(b×c), which can change the operation order in multiplication. Multiplicative associative law is not widely used in daily life, but mainly plays a simple role in some complex operations.
Multiplication principle: If the dependent variable f is in direct proportion to the independent variable X 1, X2, X3...Xn, and each independent variable is qualitatively different, if any independent variable f is missing, it will lose its meaning, which is called multiplication.
In probability theory, the result of an event needs to be divided into n steps, the first step 1 includes M 1 different results, the second step includes M2 different results, …, and the n step includes Mn different results. Then this event may have n = m 1× m2× m3×…× Mn different results.
Addition principle: If the dependent variable F and the independent variable (z 1, z2, z3…,? Zn) is directly proportional to each other, and each independent variable has the same mass. If the dependent variable f still makes sense without any independent variables, it is addition.
In probability theory, if an event has n kinds of results, the first 1 result includes M 1 different results, the second result includes M2 different results, ... and these n kinds of results include Mn different results, then this event may have n = M 1+M2+M3+...+Mn different.
The quality mentioned above is divided according to the function of independent variables.
This principle is the quantitative expression of logical multiplication and logical addition.