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The Number Patterns And Sequences

Updated on August 20, 2019
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Whole Numbers and Integers
Whole Numbers and Integers
Prime Numbers
Prime Numbers

Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Prime numbers and The Fibonacci Sequence.

The purpose of this article is to discuss the number of patterns and sequences.

Let begin with the definition of Whole number and Integers.



1. Whole Numbers and Integers

Definition :

Whole Number - A number without fraction and sometimes we called it Integers.

Integers - A number without fraction and consist of positive integers and negative integers.


What is the difference between the whole number and Integer?

The whole number include all-natural numbers that begin from 1 onward.

Therefore, is ZERO a whole number?

The answer is YES. Mathematicians have defined Whole numbers as the collection of non-negative integers, which including Zero.

Zero is neither positive integers or negative integers. Zero is located in between positive integers and negative integers.

Remember this :

A positive integer - a number which is more than zero.

A negative integer - a number which is less than zero.

To help us understand the difference between the whole number and integer, take a look at the examples below :

1. Is 0.1 a whole number?

Solution: No, 0.1 is not a whole number because it is a fraction.

2. Is 0.1 an integer?

Solution: Yes, 0.1 is a positive integer because it is more than 0.



2. Odd Numbers and Even Numbers

Odd Number is the number that always ends with 1,3,5,7,9. The first odd number is 1 following by 3,5,7,9 and so on...

Even Number is the number that always ends with 2,4,6,8,0. The first even number is 2 following by 4,6,8.10 and so on...



3. Rational Numbers and Irrational Numbers.

Definition: A rational number is a number that can be written in ratio forms such as p/q, where p and q are integers and q ≠ 0. Examples of rational numbers are 1/2, 0.5, 5. Remember, every integer is a rational number.

How about Irrational Numbers?

In the Mathematics field, the irrational numbers are all the real numbers which are not rational numbers. Examples for irrational numbers are Π (Pi = 3.14159265...), 0.03030303..., The square root of 5 and so on.



4. Prime Number


What is Prime Number?

How to prove whether a number is a Prime number or not a prime number?

The Basic concept of the prime number - Prime number is a number that is divisible only by itself and one.

Therefore,

Number One is not a PRIME number!

To identify the prime number, just remember these rules :

(a) Number one is not a prime number.

(b) All EVEN numbers are NOT a prime number EXCEPT number two.

(c) All numbers that ended with 5 are NOT a prime number EXCEPT number five.

(d) All prime numbers are odd number except the only one - number TWO!

Here, we make a list of Prime Numbers from 1 to 100 :

2 (the only even number), 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

What is the usage of Prime numbers?

In the modern-day, prime numbers are very useful in cryptography!


5. The Fibonacci Sequence.

People are familiar with quite a few math sequences like Prime numbers, odd numbers, and even numbers.

One of the popular math sequences is The Fibonacci Sequence.


What is the Fibonacci Sequence?

Let us start with a series of numbers : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ....

How to form these numbers?

It is simple. The first number is 0, the second number is 1, the next number in The Fibonacci sequence is found by adding up the two numbers before it.

First number = 0

Second number = 1

Third number = 0 + 1 = 1

Fourth number = 1 + 1 = 2

Fifth number = 1 + 2 = 3

Sixth number = 2 + 3 = 5

Seventh number = 3 + 5 = 8

Eighth number = 5 + 8 = 13

Ninth number = 8 + 13 = 21

Tenth number = 13 + 21 = 34

and so on...

This is how we formed the Fibonacci Sequence - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ....


What is the real-life application of the Fibonacci Sequence?

In daily life, we can use the Fibonacci numbers to calculate from Miles to Kilometres and vice versa.

Comments

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    • verdict profile image

      George Dimitriadis 

      7 months ago from Templestowe

      Hi.

      Your article has covered quite a lot. A number of points worth pointing out.

      You need to define 'real numbers'.

      It is stated that 0.1 is not a whole number because it is a fraction. Perhaps you should write it as 1/10

      You state that 'Prime number is a number that is divisible only by itself and one', but by this definition the number 1 will be prime because it satisfies the definition. You need to include 'different', such as

      'A prime number has two different factors; itself and 1'.

      At the end it is mentioned that Fibonacci numbers can be used to convert miles to km. I'm not sure how this can be done.

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