subject: Integres - The Basic Building Blocks To Mathematics [print this page] Types of Numbers: Types of Numbers:
Natural Numbers (N):
The first kind of numbers everybody learns, are called the counting numbers or natural numbers. These numbers, obviously, are given as:
1, 2, 3, 4, 5, 6,..
So, the smallest natural number is 1 and the largest natural number can not be found or in mathematical language it is called infinity. The symbol for the natural number is N. Natural number can be shown in a group as follows:
N = {1, 2, 3, 4, 5,}
Whole Numbers (W):
If zero is included to the natural numbers then the new group of numbers is called the whole numbers. The symbol used to denote the group of the whole numbers is W.
W = {0, 1, 2, 3, 4, 5, }
OR W = 0 + N
As it is clear from the above group, the smallest whole number is 0 and again the largest whole number is infinite or undefined.
Indians found the number 0 and it became very easy to write very large numbers, such as millions, billions and trillions.
Now, the question arises, what about some values below zero? Such as, very often in winter, the temperatures go below zero in many parts of the world. Some buildings have parking floors underground, if ground level is zero, what number
Normally height of mountains or other higher regions is calculated considering the sea surface level as zero. What about the depth which is below the sea surface level? Our bank accounts normally have some money we deposited, and if we withdraw all the money we deposited in to our account, the account balance becomes zero. What if we have overdraft limit, that is, we borrowed from the bank.
So, there are lots of more examples in our daily life where whole numbers are not helpful. Therefore mathematicians found another set of the numbers and name this set Integers.
What are Integers?
Integers include the whole numbers as well as the negative numbers. Mathematicians developed the concept of the negative numbers to deal with the problems you read in above examples. The negative numbers are the additive inverse (negative of a Natural number and when added to number gives zero) of the Natural numbers. For example the additive inverse of 1 is 1, so that, 1-1 = 0 or additive inverse of 2 is 2 and so on. The integers are denoted by the symbol "I" or "Z".
I = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
Notice that integers contain all the natural numbers as well as whole numbers. In other words all the whole numbers (including natural numbers already) are integers too. But, are all the integers whole numbers? The answer is no, as whole numbers do not have negative numbers in them while integers do. So, it can be said that all the whole numbers are integers but all the integers are not whole numbers.
Notice another thing, number 0 is neither positive nor negative and is called the neutral integer. Right side to zero is the positive integers (or the natural numbers) and left side to zero are negative integers.
Look, positive sign is not shown in front of any of the positive integers, so remember that any number without a sign actually has positive sign in front of it and which need not to be shown, as this is understood in math all over the world. Remember, 2 is actually +2 or 3 is +3 and same for every other positive integer.
We have couple math workbooks on sale at our site, www.algebrapre.com , visit the site to downoad fractions workbook or elementary math workbook.
Integres - The Basic Building Blocks To Mathematics
