It is the smallest number, s, such that x <= s for any element, x, of the set; and if e is any number, however small, then there is at least one element in the set such that x > (s - e) : that is, (s - e) is not an upper bound.
No, it is not.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
The Real numbers
It is the rational numbers.
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.
a real numbers computable if it is limit of an effectively converging computable sequence of a retional supremum infimum computable if it is supremum of computable of sequence of a rational numbers
No, it is not.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
Yes - the set of integers is a subset of the set of rational numbers.
The Real numbers
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
It is the rational numbers.
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.
Both rational numbers and integers are subsets of the set of real numbers.
No; there are infinitely many rational numbers.
The set of rational numbers is the union of the set of fractional numbers and the set of whole numbers.
Yes, rational numbers are larger than integer because integers are part of rational numbers.