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Thread: Undefined

  1. #1
    Super Member harpazo's Avatar
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    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?
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    Forum Admin topsquark's Avatar
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    Re: Undefined

    Quote Originally Posted by harpazo View Post
    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.

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    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.
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    Forum Admin topsquark's Avatar
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    Re: Undefined

    Quote Originally Posted by Debsta View Post
    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?"

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    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".
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  6. #6
    Super Member harpazo's Avatar
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    Re: Undefined

    Quote Originally Posted by Debsta View Post
    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?
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    Super Member harpazo's Avatar
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    Re: Undefined

    Quote Originally Posted by HallsofIvy View Post
    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?
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  8. #8
    Super Member harpazo's Avatar
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    Re: Undefined

    Quote Originally Posted by HallsofIvy View Post
    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?
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    Re: Undefined

    Quote Originally Posted by harpazo View Post
    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".)
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  10. #10
    Super Member harpazo's Avatar
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    Re: Undefined

    Quote Originally Posted by HallsofIvy View Post
    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".)
    Thanks. I misread your reply the first I read it.
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