As much as we generally know that numbers start from 0 upto 9 and we can possibly build other numbers using those 10, there are also numbers before 0 and there are numbers between 1 and 2. This blog post aims to detail those numbers and their nature. You need to be familiar with these numbers for a couple of reasons:
- For refence purposes. i.e. to have a common name
- To know their different treatment and transition
Below is a brief discussion of:
- Natural numbers
- Whole numbers
- Integers
- Rational numbers
- Irrational numbers
- Non real numbers
Natural numbers
These are the most common numbers, if you ask anyone what are numbers? They probably would tell you about these ones. They are numbers that start from 1 and never end as they say “numbers never end”, mathematically we say they start from 1 upto infinity. The second feature is that they increase by one, from 1 we have 2;3;4;5 and so forth increasing by one from the previous number. Refer to math study guide to find out about their symbol, do this for the rest of the types of numbers.
Whole numbers
as the name goes (whole), these numbers include zero into the natural numbers. The natural numbers are not whole because they leave out the number 0. So, these ones start from 0 and likewise, they never end. They also increase by one from the previous number, starting from 1 upto infinity, 0;1;2;3;4 and so on.
Integers
Numbers never end, do they… once again we add more numbers. To make integers we take whole numbers and add to their left all the negative numbers. Negative 1, negative 2;3;4 and so forth. This means integers start from negative infinity to positive infinity, increasing by one from one number to the next number.
Notice how this has been a flow of just adding more numbers to the system, from natural numbers we add zero and then we have whole numbers, once again we add the negative numbers and we have integers.
Rational numbers
Rational means something in relation to logic right, but that English. In maths it means a number that can be expressed as a ration of whole numbers. Notice how we once again modify another type of number to get the other. If we divide a whole number and get a fraction, a terminating decimal number or a recurring decimal number, we have a rational number. For example, ½; 3.05; 3.333333.
Irrational numbers
Obviously, they are the direct opposite of rational numbers. They cannot be expressed as a fraction, terminating decimal number or a recurring decimal number. Their simplest form can be written as a decimal which after comma, has continuous numbers.
No real numbers
They are not real, they don’t exist. These numbers will give you math error if you put them on your calculator, for example square root of negative 2. All the even roots of a negative number a non-real. An even root is the square root, the 4th root, the 6th root and so on.
Concluding remarks:
That’s it with numbers and their nature, do more homework using your study guide and know their symbols and more examples.
Operating Disclaimer:
This blog post is not the first step towards learning the concepts of math but the coupling step to ease the use of your study guide and other study material. Read it over and over again to keep the concepts at the back of your head. Math is a subject of rules; know the rules, be able to duplicate them on a blank paper and go fetch your distinction.