Q: Why a mixed numbers is not in the set of integers?

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A mixed number consists of a whole number and a fraction, and it cannot be represented as a single integer or whole number. In the set of integers, only whole numbers and their negative counterparts are included. Similarly, in the set of whole numbers, only positive integers and zero are included. Mixed numbers do not fit into either of these categories.

No. They would then be mixed numbers, not integers.

The set of integers includes the set of whole numbers. The set of rational numbers includes the sets of whole numbers and integers.

Yes - the set of integers is a subset of the set of rational numbers.

The set of natural numbers is a subset of the set of whole numbers. The set of whole numbers is a subset of the set of integers. So the set of integers is the largest of these three sets.

Related questions

Mixed numbers and integers are different things.

No, the set of mixed numbers is a subset of the set of rational numbers. For example the mixed number 1 Â¼ is the same as the improper fraction 5/4 [a rational number]. Note that it is a subset, because integers are also rational numbers, but a mixed number will not be an integer. Also, any fraction between 0 and 1 will not be a mixed number.

A mixed number consists of a whole number and a fraction, and it cannot be represented as a single integer or whole number. In the set of integers, only whole numbers and their negative counterparts are included. Similarly, in the set of whole numbers, only positive integers and zero are included. Mixed numbers do not fit into either of these categories.

No. They would then be mixed numbers, not integers.

The set of integers includes the set of whole numbers. The set of rational numbers includes the sets of whole numbers and integers.

The set of integers is the same as the set of whole numbers.

Yes - the set of integers is a subset of the set of rational numbers.

The set of natural numbers is a subset of the set of whole numbers. The set of whole numbers is a subset of the set of integers. So the set of integers is the largest of these three sets.

The Natural numbers is the set of Integers greater than 0 (ie {1, 2, 3, ...})

Real numbers consist of rational numbers and Irrational Numbers.The set of irrational numbers is not divided into any coherent subset.The set of rational numbers comprises integers and other rational numbers.The set of integers comprises negative integers and [Peano's] axiomatic integers.The set of axiomatic integers comprises zero and positive integers (counting numbers).

Whole numbers or integers such as 379 are not normally expressed as mixed numbers.

Because that is how the set of integers and the set of rational numbers are defined.