Are all natural numbers also whole numbers?
Numerals are the mathematical figures used in financial, professional as well as a social field in the social world. The digits and place value in the number and the base of the number system determine the value of a number. Numbers are used in various mathematical operations as summation, subtraction, multiplication, division, percentage, etc. which are used in our daily businesses and trading activities.
What are numbers?
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Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc. which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system.
Numbers generally also known as numerals are the mathematical values used for, counting, measurements, labeling and measuring fundamental quantities.
Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2,4,7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
Types Of Numbers
There are different types of numbers categorized into sets by the number system. The types are described below:
- Natural numbers: Natural numbers are the positive counting numbers that count from 1 to infinity. The subset doesn’t include fractional or decimal values. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N=1,2,3,4,5,6,7,……………
- Whole numbers: Whole numbers are positive natural numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set can be represented as W=0,1,2,3,4,5,………………
- Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z‘. The set of integers can be represented as Z=………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can also be expressed in the fractional form in some cases. It can be expressed as 2.5,0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.
What are Whole Numbers?
The whole numbers are the numbers without fractions and are a collection of positive integers from 0 to infinity. All the whole numbers exist in number lines. All the whole numbers are real numbers but we can’t say that all the real numbers are whole numbers. Whole numbers cannot be negative. The whole numbers are represented by the symbol “W”.
Examples of whole Numbers
Natural numbers are also known as counting numbers including zero are parts of whole numbers, such as 0,1,2,3,4,5, etc. excluding negative integers, fractions, and decimals.
0, 15, 16, 76, and 110, etc. all are examples of whole numbers.
Are all natural numbers also whole numbers?
The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals.
Natural numbers are the positive counting numbers that count from 1 to infinity. The subset doesn’t include fractional or decimal values. The set of natural numbers can be represented as N=1,2,3,4,5,6,7,……………, etc. whereas, whole numbers are positive natural numbers including zero, which counts from 0 to infinity. Whole numbers also do not include fractional and decimal values.
Since, natural numbers follow all the properties of whole numbers and whole numbers contain all the numbers contained in the set of natural numbers, hence, all the natural numbers are also whole numbers, but its vice versa, i.e. all the whole numbers are natural numbers is not true, because whole numbers include one extra number which is 0.
Question 1: Is 23/19 a whole number?
No, 23/19 is a fractional value and the set of whole numbers does not includes fractions.
Question 2: Is 0 a whole number?
Yes, 0 is a whole number, because it is a real counting number and can be represented in the form of p/q with q = 1.
Question 3: Is 3/9 a whole number?
No, 3/9 is a fractional value and the set of whole numbers does not includes fractions.
Question 4: Is 28/17 a whole number?
No, 28/17 is a fractional value and the set of whole numbers does not includes fractions.