Of course not. The square root of 2 is less than 3, and (pi) is less than 4 .
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The number 1 is neither prime nor composite.
Yes, natural numbers are the set of "counting numbers" - integers bigger than zero. Hence they are all real numbers.
It is not always easy to tell if a number is irrational. If a number can be expressed as a ratio of two integers, then it is rational. If not, it is irrational. So the expression is in the negation: a number than cannot be expressed as a ratio of two integers.
-- 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.
There is no such number. Irrational numbers are infinitely dense. Given any number near 13, there are more irrational numbers between that number and 13 than there are rational numbers in all.