The product of 2 rationals must be rational.
The product of a rational and an irrational is irrational (unless the rational is 0)
The product of two irrationals can be either rational or irrational.
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In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
Rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions
It is true and false. It cannot be proved.
yes
For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.