Are disjoint and complementary subsets of the set of real numbers.
Are in the set of real numbers.
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
The set of real numbers.
Yes. All rational numbers can be changed into fraction form, while all numbers that can't are irrational.
The Real numbers
All rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions.
There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.
No, a number is either rational or irrational
the set of real numbers
It is the set of Real numbers.
All irrational numbers, complex number and so on.
The real numbers.