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2006-09-15 01:42:50 · 22 answers · asked by Anonymous in Science & Mathematics Mathematics

22 answers

Any number other than zero, divided by zero is undefined: for example, 7/0 is undefined because there is no number by which you might multiply zero in order to obtain a product of seven. Since zero multiplied by any number is still zero, 0/0 is an indeterminate form which is not the same as being undefined. This, by the way, is not useless trivia.

Those who are convinced that 0/0 is not an indeterminate form may be unfamiliar with L'Hopital's rule.

2006-09-15 02:27:12 · answer #1 · answered by tom d 2 · 1 1

I am going to try and help you find the answer yourself, okay?

Think about what the operation of division means. It is in fact defined only in terms of repetitive subtraction. Let's illustrate this by means of an example:

250.23/80 :

For integral part:
250.23 - 80 = 170.23 [1]
170.23 - 80 = 90.23 [1]
90.23 - 80 = 10.23 [1]
Total = [3] (*)
Now for fractional part:
102.3 - 80 = 22.3 -------->[1] (*)
-------> 223 - 80 = 143 ----------[1]
-------> 143 - 80 = 63 ----------[1]
-------------------------------> Total = [2] (*)

You can continue this process of subtraction until you find the number of digits you desire.

The decimal representation is given by (*), i.e. 3.12...

The division algorithm is not that difficult to apply. However, questions arise about the stopping condition. When do you in fact stop? Division is a finite process that deals with finite quantities. Since there is no clear definition for a stopping condition in a division algorithm, it is difficult to apply this in the case of 0/0. Do you stop when there is no remainder? Or do you stop after a fixed number of steps? When do you stop?
Since the application of this algorithm to 0/0 yields uncertain results, it is undefined for 0/0.

Is it not strange that the so-called smart academia (who are really stupid beyond belief) still don't even have a sound division algorithm?

Suppose that we had a number system in which all numbers could be represented finitely. In this case, we could say the stopping condition might be when there is no remainder.
This would make perfect sense. It is however not possible because numbers such as pi, e, etc will always cause problems for us.

Challenge your idiotic lecturers and professors to provide a sound division algorithm in which the stopping condition is clear and unambiguous.

This should be sufficient food for thought.

If some arrogant professor tells you it is defined, challenge the fool as follows: Ask him to provide an algorithm that works for 1/3 in decimal with a clear stopping condition. Do not accept an answer that says a repeating pattern is a stopping condition because in base 3, this algorithm does not work. Also do not accept that zeroes are a repeating pattern.

Azeem: Is mathematics about voting? What is 0/a (a <> 0)? Why is this 0? If you apply the division algorithm to this, it fails, i.e. ambiguous stopping condition.

When there is no clear stopping condition in the division algorithm, should you say the operation is undefined?

2006-09-15 03:09:29 · answer #2 · answered by Anonymous · 0 1

0/0 is not undefined. It's an indeterminate form (see the source below for a detailed exploration of this idea).

1/0 is undefined because its limit *consistently* diverges to infinity.

0/0 does not consistently diverge to infinity. For example the limit of x/x as x->0 is 1 whereas the limit of x^2/x as x->0 is 0.

Additionally, 0^0 *is* defined as 1.

So there you are. 0^0=1. 1/0 is undefined. 0/0 is indeterminate.

Any other vocabulary simply isn't correct.

2006-09-15 02:47:18 · answer #3 · answered by Ted 4 · 2 1

OMG, man, you cannot divide by zero in the Real numbers set, there is no answer, 0/0 is undefined.

2006-09-15 02:41:42 · answer #4 · answered by Anonymous · 1 1

in case you in basic terms ask 0/0 without specifying something else, this answer is in basic terms "undefined." in spite of the undeniable fact that, you'll study on your later education that it relies upon on the "importance" of 0. you need to look up something referred to as L'Hopital's rule. L'Hopital's rule, is impressive summarized with this party: imagine about lim x->0 of (x^2)/(x) in case you plug 0 in for x, you receives 0/0. in spite of the undeniable fact that, you recognize that between the x's will cancel from both the denominator and the numerator. to that end, lim x->0 of (x^2)/(x) might want to be simplified as lim x->0 of x, so it really is an same as 0. L'Hopital's rule surely asks, "to what degree (or skill) is this time period 0?" or "how 0 is this?" frequently, the solutions you receives are both infinity, 0, or some consistent. We already coated the case the position you receives 0. Now enable's see the way you get the others. Infinity: lim x->0 of x/(x^2), you get a million/x so this is going to infinity. consistent: lim x->0 of 3x/x, you receives 3, a consistent. it style of feels unusual, certain, yet you ought to study it in a unmarried of your first calculus education.

2016-11-27 00:20:48 · answer #5 · answered by Anonymous · 0 0

Its neither one nor zero. Its indeterminate.

There's a special word for stuff like this, where you could conceivably
give it any number of values. That word is "indeterminate." It's not the
same as undefined. It essentially means that if it pops up somewhere,
you don't know what its value will be in your case. For instance, if
you have the limit as x->0 of x/x and of 7x/x, the expression will have
a value of 1 in the first case and 7 in the second case. Indeterminate.

2006-09-15 02:44:10 · answer #6 · answered by king2006 2 · 1 1

0/0 is indeterminate form. If 0/0 is got from an equation it can be solved by using limits.

2006-09-15 03:35:50 · answer #7 · answered by GVK 1 · 1 0

well ramanujan had asked the same question to his teacher .... he never got an answer...
well, practically i would vote for the answer to be 1, but in the scientific world it clearly been described as an undefined situation... because nobody has been able to bring about a situation where 0/0.....

2006-09-15 03:32:17 · answer #8 · answered by azeem 2 · 1 1

It is neither 0 nor 1 it is UNDefined

2006-09-15 02:24:08 · answer #9 · answered by Mein Hoon Na 7 · 1 1

Any number by zero [0] is not defined.

2006-09-15 03:08:12 · answer #10 · answered by Lady_Marmalade 2 · 1 1

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