what would be the result if a real number is divided by zero?I want to know about recent achievement on it?

Question

As far as I know the result is undefined till now. But I don't know about the recent researcg going on it .

Answer 1

Any real number not equal to zero or conditioned as approaching infinitude can be divided by zero without strict adherences to not being defined.
It's like this, for a sufficiently large X
1/X = Y
Gives a very small Y.
In other words lim 1/x ->0
x->infinity
The converse is also true in that
for a non zero real number a,
a/0 = a. (1/0) = a. lim 1/x = a.infinity -> infinity
x->0
The approach to infinity is perhaps positive or negative depending on the sgn of a.
What is undefined are limits like infinity/infinity or zero/zero and zero/infinity or infinity/zero.
Some of these however in functional form can in fact be evaluated using results in analysis like L'Hopital's rule which is valid for the entire complex field.
As for research, there's not much directly on this. However in 2003 a regularised result for the infinite product was put forth in which (infinity)! = V(2pi)
and a recent discovery is the normalisation of the prime product
to infinity = 4(pi)^2

Hope this helps!

Answer 2

Dividing by Zero Can Get You into Trouble!
If we persist in retaining such errata in our educational texts, an unwitting or unscrupulous person could utilize the result to show that 1 = 2 as follows:

(a).(a) - a.a = a2 - a2
for any finite a. Now, factoring by a, and using the identity
(a2 - b2) = (a - b)(a + b) for the other side, this can be written as:

a(a-a) = (a-a)(a+a)

dividing both sides by (a-a) gives

a = 2a

now, dividing by a gives

1 = 2, Voila!


This result follows directly from the assumption that it is a legal operation to divide by zero because a - a = 0. If one divides 2 by zero even on a simple, inexpensive calculator, the display will indicate an error condition.
Again, I do emphasis, the question in this Section goes beyond the fallacy that 2/0 is infinity or not. It demonstrates that one should never divide by zero [here (a-a)]. If one does allow oneself dividing by zero, then one ends up in a hell. That is all.

Answer 3

In general, the result is undefined. It may be useful to call it infinity, if that is allowed in your answer space; but if you cannot accept infinity as a possible answer, then it is undefined.

No research is required on this. Mathematicians are perfectly happy with their current rules about what happens when they divide by zero, or try to. There are no outstanding problems, open questions, or uncertainties. The whole thing is completely understood. The only part that is not understood is why so many non-mathematical people think that there might be a problem somewhere in it.

Answer 4

Any number divided by "Zero" is always undefined" . Remember dividing is the opposite of multiplication so take a look at it this way. 10/0= undefined... in the same sense Another way of looking at this is this: to check your answer you would multiply a number times zero that should equal 10, but since anything times zero is zero this does not check. This is why any number divided by 0 is considered undefined. :)

Answer 5

Think about what division means. 0 times anything is 0. And for example, 12 divided by 4, you are asking "4 times what is 12?" The answer is three, of course. Well ask yourself "0 times what is 4?" (for the problem 4 divided by 0) and of course there is nothing because anything times 0 is 0. So therefore it is undefined. There is no research and no question, division by 0 is undefined. I teach math at a university and I am sure of this.

Answer 6

dividing by zero is a very simple topic in calculus. there are only 3 possible results when you divide a REAL number by 0...

Let x be a positive real number.

Computing for x/0 is nonsense, but you may find
lim a->0 (x/a) instead. It is one of the postulates in calculus that it tends to infinity.

Let x be a negative real number.

Likewise, computing for x/0 is nonsense, but you may find
lim a->0 (x/a) instead. It is also one of the postulates in calculus that it tends to -infinity.

When x = 0, then the result 0/0 is another form. It is an "indeterminate" form. because 0/0 may have values from -infinity to +infinity (including zero). 0/0 is common in calculus.

^_^

Answer 7

if a real number is divided by zero it would still tend towards infinity (i am a maths graduate)

the following is the reason why

take a number and divide by 1

x/1 = 1

then divide by something smaller

x/0.1 = 10x

so as the denominator decreases the overall answer increases

x/0.01 = 100x

x/0.001 = 1000x

etc

so as the denominator approaches zero the value increases towards infinity (rather than zero or nothing)

but in practice you would just use the symbol for infinity which is like an '8' on its side

Answer 8

Zero is an invention. Division by zero is not permitted. You can say the result of division by zero is infinity.meaning thereby that if the denominator becomes smaller and smaller the resultant is going to be bigger and bigger.1/10000 is smaller than 1`/1000.

Answer 9

a real number divided by zero is meaningless in mathematics.it can
give quite absurd results 1=2 proved above.

Answer 10

If the number is positive then the answer is infinity
If the number is negative then the answer is -infinity
If the number is 0 the result is unknown
If the number is infinity the result is infinity
If the number is -infinity the result is -infinity