Is the expression 0/0 ( zero divided by zero) meaningless or does it equal zero? Explain?

Question

please explain these question, or give my the exact source

please also , when you explain to me please dont say that when you put 0/0 in the calculator blah......... i would like a real explination thank you

Answer 1

Division by zero is not meaningless, and it does not equal infinity as some would have you believe

The problem is we do not know what the answer is, so, since Einstein, we say

0/0 is undefined!

Answer 2

Despite calculators and computers often describing it as an "illegal operation", there is no law against it. The simple answer is that the result is unknown.

Suppose you attempt to divide one by zero. Let the quotient (the result after dividing) be q.

As 1/0 = q, it follows that 1 = 0×q = 0, which is absurd. In fact it can be seen that any non-zero quantity, r, divided by zero would lead to the same contradiction: r, a non-zero value, is equal to zero.

This would suggest that calculators and computers got it right. However, if we consider the special case, 0/0 = q, we get, 0 = 0×q = 0, and this does not seem to lead to a contradiction. So is it okay to divide zero by zero?

Consider the well known algebraic identity,

x^(n)–1 = (x–1)(x^(n–1)+x^(n–2)+ ... +x^(2)+x+1)

Rearranging, (x^(n)–1)/(x–1) = x^(n–1)+x^(n–2)+ ... +x^(2)+x+1.

If we let x = 1, this leads to, 0/0 = 1 + 1 + ... + 1 = n; that is, we can show that 0/0 can be equal to any natural number you choose and so the value of 0/0 is unknown.

Previously we showed that, r/0 = q, where r is not equal to zero, leads to the contradiction, r = 0. This supports the fact that any non-zero value divided by zero is not equal to a finite value. However, there remains one other possibility: the result of dividing by zero is not finite, but infinite.

Consider the ratio, 1/x as x gets closer to zero.

1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
and so on.

This suggests that as x tends towards zero, 1/x tends towards infinity. However...

1/-0.1 = -10
1/-0.01 = -100
1/-0.001 = -1000
and so on.

That is, as x tends towards zero (from a negative direction), 1/x tends towards negative infinity.

So which is it? Does 1/0 = ∞ or does 1/0 = -∞?

To resolve this quandary, we say the anything divided by zero is unknown, or indeterminate: there is no reason why it should be equal to any one particular value over the other possible choices.

Answer 3

Zero divided by zero is called INDETERMINATE. It is a special case of something devided by zero. (which is usually invalid) It means it can be any number.

Think about this:
Let the answer of 0/0 be A, then the formula is
0 / 0 = A
If you turn this around, you can also say:
0 * A = 0

Now think.... what number can A be? What number of A would make this formula valid?

Any number of A would make this formula valid, because anything multiplied by zero is zero. It can be real number, imaginary number, just anything.

That is why it is called indeterminate. You cannot determine it. You will learn about this when you get to college and study calculus. Here's the answer, since you asked.

By the way, if you have NOT gotten to this level of math, the correct answer is "UNDEFINED." If you say 0/0 = 0, that means the number zero, which is a number, is the answer. No, the formula itself is invalid, so there IS no answer.

If this was the test question, you'd actually write UNDEFINED somewhere other than directly left of the equal sign, since the word UNDEFINED is not a number, it can not be equal to something. Therefore, you cannot write it on left or right of the equal sign.

Answer 4

As almost everybody has said, it is undefined.

The notion of an 'indeterminate form' is different - that has to do with limits, an not to do with the actual definition of 0/0. For example, 0^0 is an 'indeterminate form,' but is almost always defined as 1.

Now, when we say, 'undefined,' we just mean that we haven't defined the value. We *could* say that 0/0 = 1, by definition. That definition would not have any value, though - it would not help us solve any problems to have this definition. You could say 0/0 is "pumpkin," if you wanted, but it wouldn't help you solve any problems or simplify any definitions or clarify any theorems where the special case x=0 is excluded.

Answer 5

0/0 is what is called "indeterminate" in mathematics. It does not have a fixed value.

In fact, if f(x) and g(x) are two function, both of which are equal to zero for some value of x = a, then one can construct examples in which the value of the limit:

lim x-> a f(x)/g(x)

can take on any value you want.

For example, if f(x) = 2*x and g(x) = x

lim x-> 0 f(x)/g(x) = 2 (by using l'Hopitals rule)

whereas for f(x) = x^2 and g(x) = x

lim x->0 f(x)/g(x) = 0

Answer 6

0/0 itself is meaningless because nothing can ever be dived by zero. However the limit of a function as it approaches 0/0 can be determined to be infinity, 0, or a real number through the use of L'Hopital's rule. because the limit of a function as it approaches 0/0 can change from function to function, it is called an indeterminate limit.

Answer 7

i am pretty sure that it is meaningless because when i type in 0/0 in my calculator it says undefined. It would answer 0 if was equal to zero.

Answer 8

ITS UNDEFINED:)