To understand the difference between an irrational number and an integer, we first need to define each term.
An integer is a whole number that can be positive, negative, or zero. In mathematical terms, integers are part of the number set that includes {…, -3, -2, -1, 0, 1, 2, 3, …}. They do not include fractions or decimal points.
On the other hand, an irrational number is a number that cannot be expressed as a simple fraction or a ratio of two integers. In other words, it cannot be written in the form p/q, where p and q are integers and q is not zero. The decimal representation of an irrational number is non-terminating and non-repeating. Examples of irrational numbers include π (pi)√2, which cannot be precisely expressed as fractions or decimals.
To summarize:
- Integers: Whole numbers, including positive and negative numbers, as well as zero (e.g., -5, 0, 3).
- Irrational Numbers: Numbers that cannot be expressed as fractions, with non-terminating, non-repeating decimal expansions (e.g., π ≈ 3.14159, √2 ≈ 1.41421…).
Both types of numbers are fundamental in mathematics but play different roles in various fields, such as number theory, algebra, and calculus.