'pi' and 'e'
No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number
Of course not. The square root of 2 is less than 3, and (pi) is less than 4 .
The square root of 2 and the square root of 3 both qualify. Both of these are irrational and both are greater than 1 but less than 2. There are, of course, uncountably infinite different irrational numbers in the range between 1 and 2 and countably infinite rational numbers.
No, the set of irrational numbers has a cardinality that is greater than that for rational numbers. In other words, the number of irrational numbers is of a greater order of infinity than rational numbers.
Yes. In fact, the cardinality of irrational numbers is greater than that of rational numbers.
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Irrational numbers are infinitely dense so that there are infinitely many irrational numbers between any to numbers. In fact, there are more irrational numbers between any two numbers than there are rational numbers in total!
Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)
Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.
Irrational numbers are real numbers because they are part of the number line.
Yes, there are.
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.