SOLIDIFYING THE CONCEPT OF NUMBERS

First, will understand, why we have numbers. Say, you are the manager of a restaurant. People sitting in the table order for 4 burgers. In the 'numberless world' , you will pass the order to the kitchen by calling out 'burger, burger, burger, burger'. We know saying 'four burgers' is easy. Four is a number. So, numbers are a shortcut for counting by ones'. Number is abstract form. Four may mean four butterflies or four stones. Numbers are concepts like beauty and intelligence.
Let us use pebbles to represent the numbers. Four can be arranged into 2*2 square form. Take 8. It can be represented by 8 pebbles arranged into 2*4 rectangular form. Many numbers can be represented by a square or a rectangle formed using pebbles. Examples 6,8,9,10,12,14....
But some numbers cannot be made into rectangle. Example 1,3,5,7,11..... These numbers which cannot subdivided into other numbers are called prime numbers. The prime numbers are 'atoms' of the number world. We can construct any number using them. How many prime numbers are there? Is there a limit for prime numbers? We do not know the answer.
Numbers should have base. We use numbers of base 10 (0.....9). Clocks use numbers of base 60. Computers manipulate binary numbers (0,1) of base 2. Base 16 numbers are also used in electronics. Even you can create your own system of numbers, if need be.
Let us solve one simple problem using pebbles to represent numbers.
Sum the numbers from 1 to 10. The answer is 55. No wonder. Let us solve it in a different way.

Put one pebble for number 1 in the first row. Put two pebbles for 2 in the second row. Repeat the process up to number 10. You will get a right angled triangle. That is half of a square, cut along the diagonal. Fill the missing 'half' with pebbles. You get 10*11 matrix of pebbles. Total elements (pebbles) in the square is 110. Half of it is 55. Hence the answer sum is 55. Hence if you picture and solidify the numbers, you can easily attack the numerical problems.
Numbers are the foundation on which Fort of mathematics is built.
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