Write down the numbers without using the symbol of Zero.
… Now what you will do????
Let me say you write the further numbers as:-
18 -> %
…. and soon you will run out of symbols. And of course it will be tediously difficult to recall and teach this writing. Do you see the HUGE difficulty in this number listing??
and so on… But this is nothing better than the listing above. WHY SO? this is also a listing of SYMBOLs , in fact an even tedious one which requires you to know and describe the addition right in the description of the numbers.
What exactly is the meaning of “11” ?
11 = 1 x 10^1 + 1 x 10^0
i.e. you take zeroth power, multiply by one, and add it to “take 1st power of ten and multiply that by one”.
This process of power of a number, is called a having a number system writing with the basis as that number.
E.g. in Binary,
11 = 1 x 2^1 + 11 x 2 ^ 0.
i.e. in binary, 11 is the way to write the number 3.
and in a system with basis as a certain number, you can only have those many symbols. e.g. you use only 0 and 1 in a binary system. and 0 to 9 in a normal decimal system. we don’t have a special symbol for “Ten”.
Lets check your understanding.
Write the number 6 in a number system with basis 5.
Could you do it?
since it is base 5, you can use only the numbers 0,1,2,3,4. to reach to 6, you have to add 1 to 5. so,
11 = 1 x 5 ^ 1 + 1 x 5 ^ 0 = 6 in the base 5.
the number 5 itself, will be written as 10.
so also, in any number system, the number which is used as the base of that system, is always written as 10.
Is this absolutely clear ??
If yes, NOW you can see the importance of ZERO. Without indicating the absence of a certain lowest power, you CANNOT have the number which is used as the basis of that system.
?? 🙂 Any revelations ?? 🙂
Without zero, the world couldn’t have counted beyond a handful of numbers. There cant be a systematic counting system.
That’s what was a wonderful contribution of India to the world.