How to prove that the irrational number is not complete - Quora. -1 / ( n * sqrt(2)) where n is a positive integer. The least upper bound of this set is 0, which is not an irrational number. So the irrationals have a nonempty subset bounded above that has no least upper bound in the set of irrationals.

Are the irrationals a complete metric space?

Irrational Number Space is Complete Metric Space.

Are there an infinite number of irrationals?

This is because π is an irrational number, which means it cannot be written as the ratio of two whole numbers. Irrational numbers aren't rare, though. ... Even between a single pair of rational numbers (between 1 and 2, for example) there exists an infinite number of irrational numbers.