All natural numbers are rational numbers.
No Irrational Numbers are natural numbers.
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The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
An integer is a whole number. There are lots of other numbers, such as fractions or rationals, and irrational numbers (such as the square root of 2)
The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.
Infinitely many! There are an infinite number of rational numbers between any two irrational numbers (they will more than likely have very large numerators and denominators), and there are an infinite number of irrational numbers between any two rational numbers.
No. "Natural" numbers are the counting numbers, otherwise known as the positive integers. They are all rational.