Identity means that the calculation result is equal to its own, such as the union operation of proposition P and empty set, and the intersection operation of proposition P and complete set;

Identity means that the calculation result is equal to the complete set or empty set, such as the intersection operation of proposition P and empty set, and the union operation of proposition P and complete set.

In abstract algebra, for any element X, if there is an element A with ax=xa=a, it is said that A is zero; If there is an element B of bx=xb=x for any element X, it is said that B is unary, just like ordinary multiplication.

For any x, 0x=x0=0, 0 is zero,

For any x, whether 1x=x 1=x, 1 is an element,

The law of zero is a formula similar to AX = XA = A. For example, for any set A, complete set E∪A=E and empty set O∪A = O, so the union operation of complete set E is equivalent to zero, and the intersection operation of empty set O is equivalent to zero, so E∪A=E, O.

Extended data:

According to the requirement of identity, there are two kinds of logical errors that violate identity: confusing concepts or stealing concepts, changing the topic or stealing the topic.

Confuse concepts or steal concepts.

In the same thinking process, if you don't use a concept in the original sense, but mix different concepts into one concept or change the meaning of the same concept, and don't keep the definition and identity of concept connotation and extension, you will make a logical mistake of "confusing concepts" or "stealing concepts"

1, confusing concepts

Conceptual confusion means that in the same thinking process, due to unclear understanding or lack of logical cultivation, different concepts are inadvertently regarded as the same concept, resulting in conceptual confusion.

2, stealing the concept

Stealing concepts refers to deliberately violating the requirements of identity in order to achieve a certain goal, and using different concepts as the same concept in the same thinking process. There are several ways to steal concepts.

First, arbitrarily change the connotation and extension of a concept to make it another concept.

Second, confuse two specious concepts.

Third, replace the set concept with the non-set concept, and vice versa. .

Fourth, the confusion caused by the use of polysemous words.

References:

Baidu encyclopedia-homology