Integer is a basic concept in mathematics, which is used to represent numbers without decimal parts. Integers include positive integers, negative integers and zero. Positive integers are integers greater than zero, and negative integers are integers less than zero. Zero is neither a positive integer nor a negative integer, but it is still an integer.

Integers can be represented by infinite numbers, such as 1, 2, 3,-1, -2, -3, etc. Integers can perform various mathematical operations such as addition, subtraction, multiplication and division.

Introduction to integers

Integers are widely used in real life. It can be used to represent population, temperature, financial data, scores, rankings and so on. Integers are also widely used in the research and application of computer science, statistics, physics and engineering.

Integers have the following characteristics:

Integers are closed under addition. The result of adding two integers is still an integer, for example, 2+3=5.

Integers are closed under subtraction. The result of subtracting two integers is still an integer, such as 5-3=2.

Integers are closed under multiplication. The result of multiplying two integers is still an integer, for example, 2×3=6.

Integers are not necessarily closed under division. The result of dividing two integers may be a decimal, such as 7÷2=3.5. But if an integer is divisible, the result is still an integer, for example, 8÷2=4.

Correlation extension

Absolute value of an integer: the absolute value of an integer is the distance from the integer to zero, which is expressed by |a|, where a is an integer. For example, |-5|=5, |3|=3. Absolute value can be used to represent the distance or size of a number, whether it is a positive integer or a negative integer.

Comparison and size of integers: the sizes of integers can be compared. If an integer is greater than another integer, the former is said to be greater; On the contrary, if an integer is smaller than another integer, it is said that the former is smaller. For example, -3

Integer representation in decimal system: Integers can be represented in different decimal systems, and the most common one is decimal system (radix 10). In addition, integers can also be expressed in binary (radix 2), octal (radix 8) and hexadecimal (radix 16). In decimal representation, the weight of each number is different. For example, in decimal representation, the weight of one digit is 1, the weight of ten digits is 10, the weight of hundreds digits is 100, and so on.

Mathematical operation of integers: Various mathematical operations can be performed between integers, such as addition, subtraction, multiplication, division and modulo (taking the remainder). These operations satisfy a series of algorithms such as commutative law, associative law and distributive law. The mathematical operation of integers plays an important role in algebra.

Summary:

Integer is a basic concept in mathematics, which is used to represent numbers without decimal parts. Integers include positive integers, negative integers and zero, and can perform various mathematical operations. Integer is widely used in real life and plays an important role in computer science, statistics, physics and engineering. Integer-related extensions include absolute value, comparison and size, decimal representation of integers and mathematical operations.