The symbol Z stands for integers. For different purposes, the symbol Z can be annotated. Z+, Z+, and Z>are the symbols used to denote positive integers. The symbols Z-, Z-, and Z< are the symbols used to denote negative integers. Also, the symbol Z≥ is used for non-negative integers, Z≠ is used for non-zero integers. Z*is the symbol used for non-zero integer.
If we are supposed to subtract one integer from another, first change the sign of the subtrahend. After this add the two numbers, with the sign of the subtrahend changed and perform according to the addition rule of integers.
While multiplying any two integers with each other, first find the product of the integers without considering the signs. After you get a product, see the signs of the two numbers you just multiplied. If the sign of both the numbers is the same, the product is positive. On the other hand, if the sign of both the numbers is different, the product is negative.
Division of integers works the same way as the multiplication of integers. While dividing any integer with another, first find the quotient of the division of integers without considering the signs. After you get a quotient, see the signs of the numbers you just divided. If the sign of both the numbers is the same, the quotient is positive. On the other hand, if the sign of both the numbers is different, the quotient is negative.
The different algebraic properties that apply to numbers apply to integers as well.
Integers follow the closure property under the operations of addition, subtraction, and multiplication. This means that for any two integers which are represented by p and q,
Additive identity is the number which when added to an integer gives the same integer.
Additive inverse is the number which when added to an integer gives zero as the sum.