What are Numbers?
We add things or objects using numbers. The numbers 1, 2, 3, … are named as counting numbers or natural numbers. The counting numbers or natural numbers accompanying zero forms the set of whole numbers.
What are Whole numbers?
The whole numbers are a portion of the number system which includes all the positive numbers from number 0 to infinity. These numbers are an imperative part of the number series.
So, they are all actual numbers. We can state that all the whole numbers are real numbers, although not all the real numbers can be termed as whole numbers.
The absolute set of natural numbers along with ‘number 0’ are called whole numbers. The examples are: 0, 11, 25, 36, 999, 15998, etc.
These numbers are positive integers consisting of number zero and they do not include incomplete or decimal parts at all.
Addition, subtraction, multiplication, division, and all other numerical operations are possible because of the presence of whole numbers.
The symbol used to denote whole numbers is with the character ‘W’ in the capital letter. W = 0, 1, 2, 3, 4, 5, 6, 45, 8, 9, 2000. . . . .
- Every natural number is a whole number
- Every counting number is a whole number
- Every positive integer including zero is a whole number
- Every whole number is a real number
What are Consecutive Numbers?
To learn consecutive numbers, one first needs to understand the idea of predecessors and successors. The number that is written directly before a number is called its respective predecessor.
The number that is addressed immediately after a number is called its respective successor. Consecutive numbers are numbers that accompany each other in sequence from the smallest to the largest number.
They ordinarily have a difference of one between every two consecutive numbers. Let’s now look at a few examples of consecutive numbers.
Consecutive Even Numbers
We recognize that even numbers are those numbers that end in these respective numbers 0, 2, 4, 6, and 8. Now let us examine the set of even numbers from 2 to 12 and draft them in ascending order.
The numbers are ordered as 2, 4, 6, 8, 10, 12 when written from the smallest to the largest in order. We can recognize that the constant difference between any predecessor-successor pair is only 2.
Consecutive Odd Numbers
We understand that odd numbers are one less or one more than the given even numbers. When we list them in ascending order, we can see that the difference between them is constantly 2.
For instance, take the numbers 3, 5, 7, 9, and 11. These are named as consecutive odd numbers because the difference between any predecessor-successor pair is only 2.
Characteristics of Consecutive Numbers
Consecutive numbers are numbers that accompany each other in sequence from the smallest number to the largest number. They usually have a difference of only 1 between every two numbers.
Below are some fundamental and standard properties stated to help understand the working and concepts of consecutive numbers:
- The contrast between any predecessor-successor pair is rooted. If we express the 1st number as n, then the consecutive numbers in the group will be n, n+1, n+2, n+3, n+4, and so on.
- For any two given consecutive odd numbers, the contrast is only 2. For instance, 7 and 5 are two consecutive odd numbers, their difference given = 7 – 5 = 2.
- For any two given consecutive even numbers, the contrast is only 2. For instance, 10 and 8 are two consecutive even numbers, their difference = 10 – 8 = 2.
- Any given numbers in a series will have a multiple of n.
- If n is a given odd number, then the whole of n consecutive numbers will be divisible by n.
I hope you enjoyed exploring whole numbers and consecutive numbers. In order to understand these topics in detail, you can explore various online learning platforms like Cuemath which gives access to interactive worksheets for free.
These interactive worksheets make learning fun and easy for students.