New formula that can divide by zero to give an integer

[shreyakmath]

New formula that can divide by zero to give an integer!

Does anybody here know about the Bhartiya New Rule of Fraction(BNRF)?
It is capable of dividing by zero!

In most elementary terms, we know that division is successive subtraction. For example 6 divided by 3 is 2 because 3 can be subtracted from 6, 2 times. Using this we can say that for example 3 divided by 0 is infinite because 0 can be subtracted from 3 infinitely many times! So how can division by zero yield an integer??

 

[sankalpmittal]

Does anybody here know about the Bhartiya New Rule of Fraction(BNRF)?
It is capable of dividing by zero!

In most elementary terms, we know that division is successive subtraction. For example 6 divided by 3 is 2 because 3 can be subtracted from 6, 2 times. Using this we can say that for example 3 divided by 0 is infinite because 0 can be subtracted from 3 infinitely many times! So how can division by zero yield an integer??

Yeah ! I too came across this thing ! I was taken aback , astounded or what to say.
Unfortunately I do not agree with this method because it has been proved in mathematics by means of calculus (and other theories) that division by 0 is undefined and we have a good reason for this.

I would like to ask other members to go through this link which explains about the method which OP has posted in his thread :
Bhartiya New Rule of Fraction(BNRF) : http://www.bnrf.co.cc/index_files/Page467.htm

Here is about the creator of this method : http://bnrf.blogspot.in/

Any comments ?

 

[Mentallic]

So in order to get his answer of 1/0=0, he has made the assumption that $\infty-\infty=0$ which is then used to show that $0/0=0$.

Good to know.

 

[Infinitum]

I think the problem with this method is that he uses approximations, instead of actual division by zero. He also bases the approximations restricted to a calculating device. For actual mathematics, there is no limit of digits and numbers are unrestricted. You can have infinite series, or a non terminating, recurring number of digits. So basically, when he does, 1/0

$$A = \frac{1}{2} (\frac{1}{-0.0000001} + \frac{1}{0.0000001})$$

But, as soon as you consider this to be infinite sequence(the above is inaccurate, for actual result, you have to consider infinite recurring decimal), you get an indeterminate form of $\infty - \infty$, and the formula fails.

 

[shreyakmath]

I can't believe how it has been accepted by the Central Board of Secondary Education in India?
Can anyone tell me what the actual formula is? I couldn't find it.

 

[Infinitum]

I can't believe how it has been accepted by the Central Board of Secondary Education in India?

Me either! :grumpy:

Can anyone tell me what the actual formula is? I couldn't find it.

It's in the slideshow sankalpmittal posted.

 

[HallsofIvy]

I can't believe how it has been accepted by the Central Board of Secondary Education in India?

Well, he says that is has been.

Can anyone tell me what the actual formula is? I couldn't find it.

No, it's not given- you have to buy the book. In fact, the whole point is to sell his book. Nothing new about that!

 

[Infinitum]

No, it's not given- you have to buy the book. In fact, the whole point is to sell his book. Nothing new about that!

In the slideshow http://www.bnrf.co.cc/index_files/Page467.htm , he did give the formula as,

According to Bhartiya New Rule for Fraction (B.N.R.F.) if +L is the largest positive and -L is the smallest negative number in calculating device along with Y ≠ ±L and X is divided by Y to give quotient A ( where given X,Y ∈ Z )

$$A = \frac{X}{2} (\frac{1}{Y'} + \frac{1}{Y''})$$

Where,
Y’ is the largest decimal value in calculating device which precedes Y and
Y’’ is the smallest decimal value in calculating device which succeeds Y.

 

[micromass]

Unfortunately I do not agree with this method because it has been proved in mathematics by means of calculus (and other theories) that division by 0 is undefined and we have a good reason for this.

One can never prove that division by 0 is undefined. It is simply a definition that one can choose to follow or not to follow. So it is appropriate to say that we choose not to define division by 0. There are very good reasons to make this choice, but it remains a choice nevertheless.

 

[dcpo]

One can never prove that division by 0 is undefined. It is simply a definition that one can choose to follow or not to follow. So it is appropriate to say that we choose not to define division by 0. There are very good reasons to make this choice, but it remains a choice nevertheless.

To expand on this, mathematicians choose axioms for things so as to be able to prove the things they think should be provable, while avoiding being able to prove things they don't want to prove (such as contradictions, or things that are not true in the system they're trying to model). In the case of arithmetic, it's not clear what division by zero should 'look like' in reality, because it doesn't obviously correspond to any meaningful concept, so we are free to define it however we want. The problem is that naive ways of defining it (along with the usual axioms for arithmetic) usually end up with problems like it being provable that all numbers are equal to each other (which clearly makes for an inadequate axiomatization of arithmetic), and ways that avoid these problems don't really give you anything extra that's mathematically interesting (for example NaN in computer science - dividing by zero won't necessarily break your program, but you can't do anything arithmetically with the result).

 

[sankalpmittal]

Man ! Here are such funny comments about that inventor.:rofl: I highly enjoyed reading them !:

http://www.thinkdigit.com/forum/random-news/142862-mystery-zero-resolved.html

I'll ask this thing in "ask Dr. Math : www.mathforum.org " and get back on here , with his comments and views regarding this.

 

[HallsofIvy]

In the slideshow http://www.bnrf.co.cc/index_files/Page467.htm , he did give the formula as,

According to Bhartiya New Rule for Fraction (B.N.R.F.) if +L is the largest positive and -L is the smallest negative number in calculating device along with Y ≠ ±L and X is divided by Y to give quotient A ( where given X,Y ∈ Z )

$$A = \frac{X}{2} (\frac{1}{Y'} + \frac{1}{Y''})$$

Where,
Y’ is the largest decimal value in calculating device which precedes Y and
Y’’ is the smallest decimal value in calculating device which succeeds Y.

So the value of X/Y will vary depending upon what "calculating device" you are using?

Essentially, then, he is redefining "X/Y" to mean "the answer your calculator gives you". In particular, with this definition, and using my calculator, 1/3= 0.33333333333333333333333333333333, 32 "3"s precisely and is not an infinite decima. Of course, if you use a different calculator, "your mileage may vary".

 

[sankalpmittal]

On a side note, my brother thought about this and persuaded me to post it here.

According to him ( in his own words below ) :

Lets divide 5 by 2. Concept wise, it is how much will each get if 5 things are divided among 2 people/things.
Lets take 5 sweets and 2 persons. That means each person gets 2.5 sweets.
Now let's take 5 sweets distributed among 1 person. Each person ( only one in this case ) gets 5 sweets.
Now let's take 5 sweets and distribute it among 0 people. So, since there are no people, hence we can say that each person ( none in this case ) got 0 sweets for there are no people to take any. Thus 5/0 =0
Coming to 0/0, we have 0 sweets and distribute it among 0 people. Since there are no people to take any sweets, all the persons ( none in this case ) get 0 sweets and thus 0/0 is also 0.

Without probing into the world of high level mathematics and physics, does this concept work ?

 

[Infinitum]

So the value of X/Y will vary depending upon what "calculating device" you are using?

Essentially, then, he is redefining "X/Y" to mean "the answer your calculator gives you". In particular, with this definition, and using my calculator, 1/3= 0.33333333333333333333333333333333, 32 "3"s precisely and is not an infinite decima. Of course, if you use a different calculator, "your mileage may vary".

This is exactly my argument about device approximations in post #4. That is what made me detest the formula. Too 'device' based and non mathematical Not to mention, untrue.

 

[HallsofIvy]

Well, that concept is one you might see to introduce division to an elementary school class. It has little to do with the concept of "division" as a mathematical operation.

And, more grammar than mathematics, the idea that "since there are no people, hence we can say that each person ( none in this case ) got 0 sweets for there are no people to take any" simply isn't correct. We could as easily say "each person got 1000 sweets" since there were no people to get any sweets anyway?

 

[sankalpmittal]

My brother :

Well yes, but the elementary division will only make the basic concepts of it.

Lets take it like this :

We are sitting on a high platform and looking down at five sweets kept on the ground. When dividing by 2, we see that two people come and take away 2.5 sweets each. If there are 0 people, we see that none came to get any sweets, means the sweets got by others is 0.

Sorry if its sounding absurd but yeah, am trying to get it from the basics.

 

[micromass]

There are 2 problems with your interpretation:

1) You did not actually divide the sweets. If I have 5 sweets in my hand and I divide them between 2 people, then everybody gets 2.5 sweets and afterwards I have no sweets left. If I divide 5 sweets between 1 person, then that person gets 5 sweets and afterwards I have no sweets left. If I divide it between 0 people, the you say that nobody gets anything. But this cannot be since afterwards I have 5 sweets left. So you did not divide it.
In fact, it is impossible to give 5 sweets to 0 people without having any left yourself. This is why the division is undefined.

2) The 0/0 situation is different. It is possible to divide 0 sweets between 0 people so that you have none left. But this is problematic. You argue that everybody gets 0 sweets. But I argue that you could also say that everybody gets 1000 sweets. Indeed, can you find a person that did not get 1000 sweets??
This is why also 0/0 is undefined as any number would be a solution.

 

[Number Nine]

In most elementary terms, we know that division is successive subtraction.

No, division by a would be better thought of as multiplication by the multiplicative inverse of a. By the field axioms, 0 has no multiplicative inverse, and so division by 0 makes no sense at all (unless you're operating under some entirely different algebraic structure).

 

[Diffy]

I feel dumber for having clicked on the link.

 

[Number Nine]

Can we safely dismiss him as a crank?

Lack of understanding of abstract mathematics? Check
Failure to demonstrate the rigour of the technique? Check
Supports technique with appeals to authority rather than a proof? Check
Has been spamming his technique all over the internet rather than submitting it a peer review journal? Check

 

[micromass]

Can we safely dismiss him as a crank?

Lack of understanding of abstract mathematics? Check
Failure to demonstrate the rigour of the technique? Check
Supports technique with appeals to authority rather than a proof? Check
Has been spamming his technique all over the internet rather than submitting it a peer review journal? Check

Yes, I think that is a nice conclusion of this thread.