Comments on: Why Can’t We Divide By Zero?

By: Tom

Tom — Mon, 09 Jan 2012 12:02:55 +0000

I always new maths teachers were frauds. great work!

By: Avi Rastogi

Avi Rastogi — Fri, 29 Jul 2011 17:55:45 +0000

I simply loved this article, as it not only gave clarification on my question, but explained things in a simplified form.
Thanks a lot.:)

By: Rob

Rob — Thu, 26 May 2011 19:04:54 +0000

I found this file on line:

http://dynamic.uoregon.edu/~teddy/OnDivisionByZero.pdf

By: Rob

Rob — Sun, 20 Mar 2011 00:47:39 +0000

The fallacy is the implicit assumption that dividing by 0 is a legitimate operation

By: N

Sat, 19 Mar 2011 16:37:21 +0000

0*1=0
0*2=0

0*1 = 0*2

0/0*1 = 0/0*2

therefore:
1=2

(wikipedia )

By: rob

rob — Sat, 05 Mar 2011 23:35:46 +0000

In mathematics the art of asking questions is more valuable than solving problems

By: rob

rob — Sat, 05 Mar 2011 21:54:01 +0000

Division is not always possible in the system of numbers consisting of the integers (6 is divisible by 2 and 3 but not by 5), but in those cases where it is, the result is always uniquely determined. In the system of all rational numbers (that is, the integers and fractions) division is not only unique but is always realizable with one exception—division by zero. On the basis of the definition of division given above, it is apparent that it is not possible to divide a number different from zero by zero. The result of dividing zero by zero, according to the definition, can be any number since c . 0 = 0 in all cases. It is usually preferable in algebra (in order not to violate the uniqueness of division) to consider division by zero to be impossible for ALL cases.

By: Rob

Rob — Fri, 04 Mar 2011 18:22:30 +0000

Definition of Division
For every real number a and every nonzero real number b, the quotient a/b is defined by:
a/b = a*1/b.

The given “Definition of Division” is merely a formal rule.

For example it tells us that we may replace 12/3 with 12*1/3.
The form a/b may be replaced with the form a*1/b.

But it does not tell us how to evaluate that division and in questions about dividing by zero the questioner must realize that this is a question about evaluating that division ie. finding a value for a/0.

For that, we must return to arithmetic, and to the relationship between division and multiplication.

If a divided by b is some number n
ie. a/b = n
then n is that number such that n times b is equal to a
ie. n*b = a.

If a/0 = n, then n*0 = a.
But n*0 = 0.
Hence, if a =/= 0,
no value of n can make the statement n*0 = a true,
while if a = 0,
every value of n will make the statement true.

Thus, a/0 either has no value or is indefinite in value.

By: Vlad

Vlad — Mon, 28 Feb 2011 23:08:12 +0000

As far as I’ve heard it, “undefined” means there is no answer (like for 1/0). However, for the case of 0/0, I’ve heard mathematicians instead use the word “indeterminate”.

In other words, it exists, but we can’t tell which one of many possible answers it is.

By: Rob

Rob — Mon, 28 Feb 2011 22:21:15 +0000

Dear Sir,

I have realized that:

One must note here that “undefined” means both not defined and indefinite.

Yours respectfully,
Rob