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
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.
The set of rational numbers is the union of the set of fractional numbers and the set of whole numbers.
No; there are infinitely many rational numbers.
In mathematics, given a subset S of a totally or partially ordered set T, the supremum (sup) of S, if it exists, is the least element of T which is greater than or equal to any element of S. Consequently, the supremum is also referred to as the least upper bound (lub or LUB). If the supremum exists, it is unique. If S contains a greatest element, then that element is the supremum; otherwise, the supremum does not belong to S (or does not exist). For instance, the negative real numbers do not have a greatest element, and their supremum is 0 (which is not a negative real number).Suprema are often considered for subsets of real numbers, rational numbers, or any other well-known mathematical structure for which it is immediately clear what it means for an element to be "greater-than-or-equal-to" another element. The definition generalizes easily to the more abstract setting of order theory, where one considers arbitrary partially ordered sets.The concept of supremum coincides with the concept of least upper bound, but not with the concepts of minimal upper bound, maximal element, or greatest element. The supremum is in a precise sense dual to the concept of an infimum.add me moshi monsters elydingle1
Yes, rational numbers are larger than integer because integers are part of rational numbers.