Zero? 7 Fascinating Question

Zero?

Here, We have 7 interesting questions.

1. If Aryabhatta invented 0 then how do we know that Ravana had 10 heads?

Ans: This is one of the biggest misconceptions in India. It has created a huge confusion among the Indians.
Aryabhatt never invented or discovered zero! He invented a unique symbol for the mathematical purpose.
Zero existed even before Aryabhatta created it as a symbol ‘0’. Zero was referred to as Shunya in Vedic times. It was always there, the counting systems. The counting systems were in words not as symbols. Our Hindu calendars and for that matter Muslim calendars has numbers.

For instance, after a new moon, there are thithis mentioned as;

Ekadasi - 1 st day of the new moon, Dwadasa - 2nd day, Tritiya - 3rd day, Chaturthi - 4th day, Panchmi - 5thday, Shasti - 6th day and so on.

2. What would be life like without zero?

Ans: We'd probably have a numerical system that has a base of 9 and -1 might take the place of zero.

Another possibility is retaining the base 10 system and having some other equivalents to zero take the place of zero.

In other words, functionally society would still be the same though mathematics would be a bit more confusing and more kids would hate the subject.

3. How do I prove 0!=1 ?

Ans: Usually n factorial is defined in the following way:

n! = 1*2*3*...*n

But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?

A first way to see that 0! = 1 is by working backward. We know that:

                1! = 1
     2! = 1!*2 
                2! = 2
     3! = 2!*3
                3! = 6
     4! = 3!*4
                4! = 24
             

We can turn this around:

                4! = 24
     3! = 4!/4
                3! = 6
     2! = 3!/3
                2! = 2
     1! = 2!/2
                1! = 1
     0! = 1!/1
                0! = 1

In this way, a reasonable value for 0! can be found.

4. Why don't teachers want us to divide zero by zero?

Ans: My 6 yr daughter is currently attending primary school. We walk to school every day and I love our morning walks where we discuss a wide range of topics like Planets, Animals, Flowers etc. She is a very curious baby.

During these talks, I figured that she is fond of numbers and enjoyed when I asked her to add numbers. I challenge her by asking not to use fingers when counting, She then imagines dots in her mind and count the dots and provide answers. We started counting in 2 ’s, 3’s, 4’s etc and developed a good foundation for multiplication and times tables. For Subtractions, we use apple problems.

I have never introduced divisions but she learned division at school, explained how to do divisions and asked me to quiz her on divisions.

When I asked her what is 6 divided by 2, she proceeded to split 6 apples into 2 baskets and came up with 3.

This morning (the reason I answered this question) she tells me

“Daddy, I found a pattern”

Me: “What baby?”

Her: “ You know 1 divided by 1 is 1, 2/2 is 1, 3/3 is 1 etc”

Me: “Wow Baby, that is a brilliant discovery!”

and then proceeded to say

“ But darling, what is zero divided by Zero?”.

The moment I completed that sentence, my mind was searching for topics to divert her attention as I did not want to say something silly but mostly did not want to say the words “Indeterminate” or “undefined”

She looked at me, Puzzled and said

“How do you want me to split no apples with no baskets? that does not make any sense daddy!”

Me (elated): “Exactly baby!!”

Me: “Exactly! It is called an Indeterminate”

Her: “Oh.. that is a difficult word”

I had a great realization that all you need is apples and baskets to solve the most complex problems... I think teachers should always find a way to explain difficult problems even when there are no solutions.

I have a huge respect for all primary school teachers, they surely have the toughest job in the world and they always come through.

5. What is the plural of zero, zeros or zeroes?

Ans: Zeros are the one used in US English while Zeroes is the one used in UK English.

So you can use both. Both are right.

6. If zero was invented by Brahma Gupta, why did people say it was invented by Aryabhatta?

Ans: What we do know is that Brahmagupta wrote the first book in which zero is treated as a number in its own right (that is, we don’t know any older book in which zero appears in that way and we don’t have much reason to believe that such a book exists and is simply lost).
The arithmetic rules he describes are quite close to our modern ones, except when it comes to the division by zero.

Before that (which includes the work of Aryabhatta) zero appears as a placeholder in place-value systems. That is, the invention of the symbol is a bit murky.
It could be that Aryabhatta “invented” the symbol but that is lost in history. The Babylonians used a place-value system as well but simply left a gap (where one would write a zero today), well until they started to use a symbol for that gap.
Whoever came up with the idea to assign a symbol for this kind of gap is lost in the mists of time.
You might as well say that it was Aryabhatta, your guess is as good as anyone. But we will never reach certainty. Unless someone invents time travel, that is.

History of mathematics, a truly fascinating topic.

7. Why is a⁰ = 1, but 0⁰ = undefined ?

Ans: This is attempting to use a division law of powers, but it is an invalid attempt. The same invalid argument can be used to prove 0³ is undefined, which we know is nonsense:

0¹ = 0 by definition of exponent 1;

0² = 0¹⁺¹ = 0¹ × 0¹ = 0 × 0 = 0;

0⁴ = 0²⁺² = 0² × 0² = 0 × 0 = 0;

0³ = 0⁴⁻¹ = 0⁴/0¹ = 0/0, which is undefined.

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