'pi' and 'e' both fit that description.
To 4.5, add the difference between the two numbers (0.1), multiplied by some irrational number that is less than 1 (or divided by an irrational number greater than 1). For example:4.5 + 0.1 / pi
You can choose an irrational number to be either greater or smaller than any given rational number. On the other hand, if you mean which set is greater: the set of irrational numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).
A prime number is a natural number that has no natural number as a factor other than itself or 1. An irrational number is not a natural number, so an irrational number can't be prime.
No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number
+sqrt(65)
the square root of 10
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.
'pi' and 'e' both fit that description.
The solution is that a is any number: integer, rational or irrational, that is greater than 2. There is no other way of putting it.
No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.
Any number which is either irrational or if rational, its simplest form has a denominator which is greater than 1.
To 4.5, add the difference between the two numbers (0.1), multiplied by some irrational number that is less than 1 (or divided by an irrational number greater than 1). For example:4.5 + 0.1 / pi
You can choose an irrational number to be either greater or smaller than any given rational number. On the other hand, if you mean which set is greater: the set of irrational numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).
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. Although the count of either kind of number is infinite, the cardinality of irrational numbers is an order of infinity greater than for the set of rational numbers.
5 is a natural number, as it is an integer greater than zero. It is a whole number, an integer, and a rational number.