is infinity a rational number or irrational number?
and why
Infinity is a quantity that can be compared with numbers, but the quantity itself is not a real number, therefore it is neither rational nor irrational.
Read more about it in:
http://en.wikipedia.org/wiki/Infinity
Infinity is neither a rational number nor an irrational number. It is not a number in the conventional sense, but rather a concept that represents an endless or limitless quantity.
To determine whether a number is rational or irrational, we need to understand their definitions. A rational number can be expressed as the ratio of two integers, where the denominator is not zero. For example, 1/3, 5/2, or -4/7 are all rational numbers. On the other hand, irrational numbers cannot be expressed as the ratio of two integers, and their decimal representations go on indefinitely without repeating. Examples of irrational numbers include √2, π (pi), and e (Euler's number).
Since infinity does not fit into either of these categories, it is not classified as a rational or irrational number. Instead, it represents a mathematical and philosophical concept of boundlessness or an unending quantity.