Question

Every integer is a whole number . True or false give reasons ?

Answer 1

Hint: We have to state that the given statement is true or false . We also have to provide the reason for the answer . We solve this question using the concept of values of integers and whole numbers . As we know the values of both we can compare the two and state that the relation is true or false .

Complete step-by-step answer:
Definition of whole numbers :
Whole numbers are defined as the collection of numbers which only have whole numbers in it i.e. its collection doesn't have any fractional value or any decimal values or any negative value . So , the collection of whole number has number in it :- $$\left\{0,1,2,3,\dots \dots \dots \dots \dots \dots \dots .\right\}$$ . The set of whole numbers don’t have any values like $$2.3,-2,{\displaystyle \frac{3}{2}}$$ etc .
The collection of values of whole numbers is also defined as the collection of natural numbers with an additional element zero .
The set of whole numbers is defined by.
Definition of integer numbers :
Integers is defined as the collection of numbers which only have perfect integer values in it i.e. its collection doesn't have any fractional value or any decimal value but it has negative values in its collection . . so , the collection of integers have values in it as :- $$\{\dots \dots \dots \dots \dots \dots ,-4,-3,-2,-1,0,1,2,3,4,\dots \dots \dots \dots \dots \dots \dots \dots .$$} . The set of whole numbers doesn't have any values like $2.3,{\displaystyle \frac{3}{2}},\sqrt{2}$etc .
The set of integers is defined by
Thus , From the definition of integers and whole numbers we can conclude that the whole numbers is a set of positive integers . Every integer is not a whole number .
Hence , the given statement is false .
So, the correct answer is “FALSE”.

Note: An integer can be positive or negative whereas whole numbers are only positive . The value of integers extends from negative infinity to positive infinity whereas the whole numbers extends from 0 to positive infinity .