In mathematics, Z represents the set of integers.
What are Integers?
Integers are whole numbers (not fractions) that can be positive, negative, or zero. They do not include decimals or fractional parts.
The Symbol ℤ
The symbol used to represent the set of integers is ℤ. This is a special double-struck capital letter "Z." According to the reference, the notation ℤ is used to denote the set of integers.
Defining the Set of Integers
The set of integers includes:
- All positive whole numbers (1, 2, 3, ...)
- All negative whole numbers (-1, -2, -3, ...)
- Zero (0)
This can be expressed mathematically as:
Examples of Integers
- Positive Integers: 5, 100, 1000
- Negative Integers: -5, -100, -1000
- Zero: 0
Examples of Non-Integers
- Fractions: 1/2, 3/4
- Decimals: 0.5, 3.14
- Numbers with radicals: √2
Where is it used?
The set of integers is a fundamental concept used in various branches of mathematics including:
- Algebra
- Number theory
- Discrete mathematics
Summary
In summary, Z or more formally ℤ is the symbol representing the set of all integers, which include all positive and negative whole numbers, and zero.