What are the concepts of operations in mathematics?

Mathematically, an operation is the act of obtaining a new quantity through a known possible combination of quantities. The essence of an operation is a mapping between sets.

For example, addition in arithmetic.

8, here. And. is the input, 8 is the result, and the plus sign "+" indicates that this is an addition operation. This is a common binary operation that is essentially a mapping in the form of AXB---C.

Other common operations include addition, multiplication, squares, and so on, which are unary operations that are essentially mappings in the form of a---b.

Algebraic operations are binary operations, mathematically defined: assuming that s and t are sets, respectively, a t-valued operation* on s

It refers to the Cartesian direct product.

s s to t is a mapping, that is, a map:

S s t is traditionally written, and for the two elements in s, a and b, we use a*b to represent this operation.

When s=t, we say that the operation is closed.

For example, s=t is a set of real numbers, and then we can define addition, subtraction, multiplication, and division operations separately.

For example, s is the set of n-dimensional real vectors, and t is the set of real numbers, and we can define the inner product.

Operation. In addition to the common algebraic operations mentioned above, there are many other operations, such as root operations, derivative operations, integration operations, convolution operations, integer operations, and so on.

These operations can be seen as the role of "operators". The so-called operator can be regarded as a function symbol that acts on an operation element.

For example, the operator of the open root operation is the root number, and the operator of the integral operation is the integral number.

Mathematically, the royal calculation is calculatedand operationsThe difference: the meaning is different, the calculation is different.

1. Different meanings: operation generally refers to the operation of formulas and functions, while calculation is generally for numbers.

Operations refer to the laws used to operate, such as addition, subtraction, multiplication, division, etc. And the calculation is more about a process, the analysis of the logarithm, the solution. The difference is that operation is a noun, whereas calculation is a verb. Demolition difference.

2. Calculation refers to the process of calculating unknown quantities based on known quantities; Computing refers to the process of making calculations according to mathematical laws. Those laws are the most basic and simple things, as well as axioms, etc., and operations can be used to extrapolate to known and unknown formulas that can simplify the calculation process, calculations, all large and small math exams are the process of calculation.

Data-to-data relationships.

If the data is in a computational formula, the data is said to have a computational relationship. Some computational relationships are determined by the intrinsic properties of the data (e.g., coefficient matrices, specific terms in series, terms in composite formulas), physical location (display or representation of data in an image, Cartesian coordinate system).

in the relationship between the curves, the CPU array, the storage of data). In mathematical calculations, data and operators.

There are specific and detailed relationships such as the number of data, the role of left and right, and the form of calculation.

"Numbers and operations" refers to understanding the consistency of integers, decimals, fractions, and meanings while understanding the consistency of integers, fractions, and fractions based on the expression of counting units. Consistency is mainly reflected in: maintaining consistency, opening up as a whole, and advancing along the core.

Cognitive consistency of number: number is the abstraction of quantity, and the concept of number is essentially empty and cautious, and the number sense and symbolic consciousness are formed.

The consistency of the operation of numbers: the operation and the relationship between the operations, the understanding of the consistency of the operation of numbers, the formation of computing ability and reasoning meaning; Consistency of number expression: number of counting units + counting unit; Consistency of the expression of number operations:

The core concept of "accumulation" of the same counting unit is the counting unit.

In mathematics, an equation refers to a formula listed when performing a calculation of a number (or algebraic formula), including numbers (or letters that replace numbers) and notation (four operations, multiplication, square, factorial, permutation, etc.). According to the different calculation methods, the calculation formula is generally divided into two types: horizontal and vertical.

Multiplication1. The same sign is positive, the different sign is negative, and the absolute value is multiplied.

2. Multiplying any number by zero gives zero.

3. Multiply several numbers that are not equal to zero, and the sign of the product is determined by the number of negative factors, when there are odd numbers of negative factors, the product is negative, and when there are even numbers of negative factors, the product is positive.

4. When several numbers are multiplied, there is a factor that is zero, and the product is zero.

5. Multiply several numbers that are not equal to zero, first determine the sign of the product, and then multiply the absolute value.

Division. 1. Divide by a number that is not equal to zero, which is equal to the reciprocal of multiplying this number.

2. Divide the two numbers, the same sign is positive, the different sign is negative, and the absolute value is divided. Zero divided by any number that is not equal to zero gives zero.

There are many ways to define the calculation of the rock calculation, there are quite precise definitions, such as arithmetic using various algorithms, also called operations, and there are also more abstract definitions, such as "calculating" the probability of two people starting in a competition.

Calculation is the process of calculating unknown quantities based on known quantities.

Calculation is the process of imitating calculations according to mathematical laws.

The calculation can be inferred that Liang Dao is known and answered, and there is an unknown.

Number concepts and number operations are two important concepts in mathematics, and they are closely related to each other.

The concept of number refers to people's concept and understanding of quantity and number, mainly including the name of number, the size of number, the reading of number, the comparison of number, etc. The concept of number is the basis of the study of Nakong macro mathematics and the premise of number operation.

Number operation is the process of adding, subtracting, multiplying, dividing, and other operations on numbers. Number operations can also be seen as the process of obtaining new number concepts by performing symbolic operations on known number concepts. For example, to add two numbers is to add them to a new number.

Therefore, the concept of numbers is closely related to number operations and is the foundation and core of mathematics learning.

In the study of mathematics, number concepts and number operations need to be combined with each other, and through the knowledge and understanding of number concepts, they can carry out correct number operations. And the results of number operations can in turn deepen the understanding of the concept of numbers. Therefore, number concepts and number operations are two inseparable parts of mathematics learning.

1. A complete list of commonly used mathematical symbols.

A complete list of mathematical symbols and arithmetic symbols of meaning.

For example, the plus sign ( ), the minus sign (-), the multiplication sign ( or ·), the division sign ( or ), the union of two sets ( ) intersection ( ) root number ( log(log,lg,ln,lb), ratio (:) absolute value sign | |Differentiation (D), integration ( ), closed surface (curve), integration ( ), etc.

Encyclopedia of Mathematical Symbols and Meaning-related Symbols.

For example, "=" is an equal sign, " is an approximate sign (i.e., approximately equal to), "is an equal sign," > is a greater than sign, "is less than a sign," is greater than or equal to a sign (can also be written" i.e., not less than), "is less than or equal to a sign (can also be written" "i.e., not greater than)," indicates the trend of variable change, " is a similar sign, " is a full equal sign, " is a parallel sign, " is a perpendicular sign, " is a proportional sign (the reciprocal relation can be used when representing inverse proportionality), "is a belonging sign," is included in the sign, " is the containing symbol, "|means "divisible" (e.g. a|.)b denotes "a divisible by b", and ||b means that r is the maximum power of a divisible by b), and any letter such as x, y, etc., can represent an unknown.

A complete list of mathematical symbols and a combination of symbols of meaning.

For example, parentheses "" in parentheses "()", curly braces "{} dash" —"=.

Encyclopedia of Mathematical Symbols and Symbols of the Nature of Meaning.

Such as the positive sign " "minus sign" - "plus or minus sign" " and the negative positive sign used accordingly ").

Encyclopedia of Mathematical Symbols and Abbreviated Symbols of Meaning.

Such as triangles ( ), right triangles (rt), sine (sin) (see trigonometric functions), hyperbolic sine functions (sinh), x functions (f(x)), limits (lim), angles ( ) because (one foot stands, cannot stand).

Therefore (he who stands on two feet can stand) (mantra: because he can't stand, so two points; Because there are two points above, there are two points below).

Sum, Continuous: , Product, Multiplication: , Extract the number of all different combinations of r elements from n elements (the total number of n elements; rThe number of elements involved in the selection), idempotent , etc.

+ Plus sign to find the sum of two numbers.

The minus sign finds the difference between two numbers.

Multiply the product of two numbers.

Division Find the quotient of two numbers.

Multiplier Find the power of several times of a number.

Prescription Find the square root of several times of a number.

d Differentiation Find the derivative (differential) of a function

Integral Find the original function (indefinite integral) of a function

The entrance door generally refers to the courtyard door. Luban ruler, one foot centimeter.

Generally, the height of the courtyard gate is 5 feet = cm.

The width of a single door is 2 feet = centimeters, and most people do 86 centimeters.

Double door 86*2=172 cm. The door of the main hall is a little smaller, generally with a Dinglan ruler, one foot 39 cm.

The height of the door is 5 feet = 39 * 5 = 195 cm, the width of a single door is 2 feet = 39 * 2 = 78 cm, and the double door is 78 * 2 = 156 cm.