What is an Endowment?

The process of assigning a value to a variable is called assignment. A statement that assigns a certain value to a variable is called an assignment statement. Each programming language has its own assignment statement, and assignment statements also have different types. The "value" assigned can be a number, or a string and an expression.

In a computer programming language, a certain assignment statement is used to implement variable assignment, and a statement that assigns a certain value to a variable is called an assignment statement. An assignment statement is used to indicate that a specific definite value assigned to a variable is called an assignment statement. In algorithmic statements, assignment statements are the most basic statements. ^[1]

A statement that assigns a certain value to a variable is called an assignment statement. Each programming language has its own assignment statement, and assignment statements also have different types. The "value" assigned can be a number, or a string and an expression.

Note that many languages use the "equal sign" (that is, "=") as the assignment number, so it may be different from that in peacetime. Pay attention when using it. ^[1]

1.Assignment format in VB

For example, to assign a value to the variable a as 12, the format is: a = 12 [Note: The variable (that is, a) can only be one letter, and the assigned value can be a formula. When it is a formula, a The value of is the result of this formula. ^[1]

2, the assignment statement in C language

Such as:

  inta; / * "Integer" type A * /
 a = 12; / * A is 12 * /

The C language requires that variables be defined before they can be used. You can also define and assign values in the same statement:

  inta = 12; / * "Integer" type A is 12 * /

3, the assignment statement in pascal language

May be slightly special. Pascal language requires variables to be defined at the beginning, and the assignment number is ": =";

  Var {variable, VARiable}
 i: integer; {i: integer;}
 Begin {begin}
 i: = 5;

...

  End {end}

4, assignment statements in easy language

Easy language is programmed in Chinese and the assignment syntax is similar to most programming languages. ^[2]

 Local variable a, integer a = 12 

5.Assignment in mathematics

Generalization of the real (or complex) absolute value over any field. The concept of assignment was first introduced by J. Kursak in 1913. Let be a non-negative real-valued function defined on any field F , and satisfy the following three conditions: ( ) = 0, if and only if = 0, and have a certain F ( ) 1; ( b ) = ( ) ( b ); ( + b ) ( ) + ( b ), J. Krsak puts such a Called an assignment on F. According to the popular name, it will be called the absolute value of F later. Soon after, A. Ostrovsky introduced another absolute value , which satisfies the above and , and called this a non-Archimedean absolute value, while satisfying , , that do not satisfy are called Archimedes absolute values. The real absolute value of the real number field R or the complex number field C is their Archimedes absolute value. A field F with an absolute value ,

Assignment

Let it be ( F , ). ^[3]

Full domain

With the absolute value of F, some analytical concepts can be transplanted to F. Let {i} be a sequence of F. If for each real number > 0, there is always a natural number n0, so that when m, nn0, there is constant (mn) <, then {i} is a of (F, ) West sequence. If for the sequence {i}, there is F, so that when nn0 there is constant (n-) <, then {i} is said to be convergent, and is called its limit. If every Cauchy sequence in (F, ) is convergent, then F is said to be complete with respect to , or (F, ) is a complete field. The real number field R or the complex number field C is complete with respect to the usual absolute values, while K. Hensel's P-number field Qp is a complete field that is not an Archimedean absolute value. The unified treatment of these two domains is a main starting point for the development of the valuation theory. The series of all shapes on F is called the series of powers of form X on literal X. According to the usual addition and multiplication operations, they form a field called the formal power series field on F, which is denoted as F ((x)). , And (0) = 0, then a complete domain (F ((X)), ) is obtained.

Assignment

When is the absolute value of Archimedes, there is the famous Ostrovsky theorem: If F is complete about Archimedes' absolute value , then F is continuously isomorphic to R or C.

Assignment

Assignments and assignment loops

The concept of non-Archimedean absolute value can also be generalized as follows. Let be an ordered commutative group whose operation is multiplication and the unit element is 1. Let 0 be a symbol, and its element r with satisfies r · 0 = 0 · r = 0 · 0 = 0, and 0 <r. If : F {0} is a full map, satisfy: () = 0 if and only if = 0; (b) = () · (b); then is An assignment of F. Or F is an assignment domain with an assignment of , denoted as (F, ). is called a value group of . When is a positive real multiplication group, is the non-Archimedean absolute value mentioned earlier. In the assignment domain (F, ), the child forms a ring, which is called the assignment ring of . The sub-ring A of F becomes an assignment ring of some value, if and only if for each element of F, there must be A or _1A.

Assignment

From a subring A of a domain F to a homomorphic map B of a certain domain K, if: For FA, there are _1A and _1B = 0; B maps the unit element of A to the unit element of K Then B is called a bit of F. Each bit of the domain obviously gives an assignment ring; conversely, it is not difficult to make a bit of the domain from the assignment ring of the domain. Therefore, the three concepts of assignment, assignment ring, and bit are closely related. Position is also an important concept in algebraic geometry, and its prototype has been in the classic works of R. Dedkin and H. Weber. Since assignment was put forward by W. Krüll in the early 1930s, the assignment theory has been widely used in algebraic number theory, class domain theory, and algebraic geometry. In the 1960s, it was increasingly associated with functional analysis.

Assignment

8. Order of assignment

Let be a group of values assigned , and be a subgroup of . If for every element of , all elements satisfying -1 < < also belong to , then is called an isolated subgroup of . Both {1} and can be used as solitary subgroups of . Let {1}. Since is ordered, all the isolated subgroups in form a complete ordered set according to the containment relationship. All isolated subgroups except itself are defined as the order of according to the ordinal type of the total ordered set formed by the containing relation. If the order of the value group of is m, is said to be an assignment of order m. Therefore, the so-called first-order assignment means that the value group has only {1} as its true isolated subgroup. The order of an ordered commutative group is 1, if and only if it is order-isomorphic to a multiplicative group made of real numbers. This fact indicates that the first-order assignment is exactly the non-Archimedean absolute value previously defined.

9. Discrete assignment definition

Let A be a propositional formula,

For all propositional variables appearing in A, give

Specifying a set of true values is called the assignment or interpretation of A. If the specified set of values makes A value true, then this group is called the true assignment of A, and if the value of A is false, then this group is called A false assignment with a value of A. ^[4]

10. Pioneering assignment

Let (F, ) be an assignment field, and K be an expansion field of F. If K has an assignment , so that for each F, () = (), then Development of on K. There is an existence theorem about the development of assignment: the assignment of F has at least one development in any extension of F.

11.Topological domain

If the domain F has a topology such that the four operations of F are continuous with respect to , then F is called the topological domain with respect to and is denoted as (F, ). The assignment domain in the Korschek sense is the earliest example of a topological domain. Assignment theory can also be studied from the perspective of topological algebra, based on the following facts. For a domain F with an absolute value , all subsets of the form {F | () <} form a basic neighborhood family of zero elements, thereby generating a domain topology of F. The situation is the same when is the assignment of F. The study of topological domain systems began with the work of D.von Danzik in the early 1930s.

12.Local compact domain

Any topological domain (F, ) can only be connected or completely disconnected. If is a locally compact topology of F, then (F, ) is called a local compact domain. Discrete topology is also a locally compact topology. As far as non-trivial and non-discrete cases are concerned, local compact regions have some significant properties. First, each local compact domain (F, ) has an absolute value , so that the topology generated by is the same as . Secondly, there is a theorem: Let (F, ) be a local compact domain. If it is connected, then it is continuously isomorphic to R or C (on the topology of the usual absolute value); if it is completely disconnected, then it is continuously isomorphic to a finite extension field of the p-number field Qp, Or a finite extended field of the form power series field K ((x)) over a finite field K.