1. Undefined

Both a/0, where a does not equal 0 and 0/0 are undefined, but for different reasons. Explain the two reasons.

Let me see...

For a/0, this is undefined because division by zero is not possible.

For 0/0, I do not know. In simple terms, why is 0/0 not defined?

2. Re: Undefined

Originally Posted by harpazo
Both a/0, where a does not equal 0 and 0/0 are undefined, but for different reasons. Explain the two reasons.

Let me see...

For a/0, this is undefined because division by zero is not possible.

For 0/0, I do not know. In simple terms, why is 0/0 not defined?
I'm not aware of a second reason. Anyway, they are both division by zero, which is undefined.

-Dan

3. Re: Undefined

I always thought that a/0 (where a is not 0) is said to be undefined, while 0/0 is said to be indeterminate.

4. Re: Undefined

Originally Posted by Debsta
I always thought that a/0 (where a is not 0) is said to be undefined, while 0/0 is said to be indeterminate.
You are probably right. Undefined being "you can't do that" vs. indeterminate meaning "we don't (can't) know what it is?"

-Dan

5. Re: Undefined

IF we were to say that a/0= b for non-zero a, we would be saying that a= 0(b)= 0 which is NOT TRUE for any b. There is no value of b that makes it true. We say this is "undefined".

If we were to say that 0/0= b, we would be saying that 0= 0(b) IS true, for any b. EVERY value of b makes it true. We say that this is "undetermined" because we cannot determine a specific value of "b".

6. Re: Undefined

Originally Posted by Debsta
I always thought that a/0 (where a is not 0) is said to be undefined, while 0/0 is said to be indeterminate.
That's the word I was looking for--INDETERMINATE. Why is 0/0 indeterminate? Is calculus needed to make known the reason?

7. Re: Undefined

Originally Posted by HallsofIvy
IF we were to say that a/0= b for non-zero a, we would be saying that a= 0(b)= 0 which is NOT TRUE for any b. There is no value of b that makes it true. We say this is "undefined".

If we were to say that 0/0= b, we would be saying that 0= 0(b) IS true, for any b. EVERY value of b makes it true. We say that this is "undetermined" because we cannot determine a specific value of "b".
He is right but why is 0/0 called indeterminate?

8. Re: Undefined

Originally Posted by HallsofIvy
IF we were to say that a/0= b for non-zero a, we would be saying that a= 0(b)= 0 which is NOT TRUE for any b. There is no value of b that makes it true. We say this is "undefined".

If we were to say that 0/0= b, we would be saying that 0= 0(b) IS true, for any b. EVERY value of b makes it true. We say that this is "undetermined" because we cannot determine a specific value of "b".
Does calculus provide a reason for 0/0, too?

9. Re: Undefined

Originally Posted by harpazo
He is right but why is 0/0 called indeterminate?
I said that: 0/0= b would be the same as 0= 0*b which is true for all b. A specific value for b cannot be determined.

Calculus doesn't need to "provide a reason for 0/0", it's arithmetic!
(Calculus does deal with limits of fractions where the limits of the numerator and denominator, separately, are 0, but that's NOT "0/0".)

10. Re: Undefined

Originally Posted by HallsofIvy
I said that: 0/0= b would be the same as 0= 0*b which is true for all b. A specific value for b cannot be determined.

Calculus doesn't need to "provide a reason for 0/0", it's arithmetic!
(Calculus does deal with limits of fractions where the limits of the numerator and denominator, separately, are 0, but that's NOT "0/0".)