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Zero division

  1. Aug 9, 2015 #1
    Dear PF Forum,
    I just read Math FAQ
    Please confirm.
    These rules are not int practice. Is this true?
    Because 30 years ago in high school, I was taught.
    x/zero is infinity, error in computer.
    zero/zero is undefined, not zero. Also error in computer.

    So zero/zero is undefined or zero?
    Thanks for anyhelp confirming my doubt.
    [Add: is not in practice today, implying that in the old days some calculation still use zero/zero = zero.
    When was it's not in practice?]
     
  2. jcsd
  3. Aug 9, 2015 #2

    micromass

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    This is wrong, something divided by 0 is undefined. Always.

    Undefined.
     
  4. Aug 9, 2015 #3
    Please confirm one more thing.
    A. ##\lim h{\to 0} \text{ } \frac{6}{h} \rightarrow \text{ infinity}##

    B. ##h = 0; \frac{6}{h} \rightarrow \text{ undefined}##

    C. ##\lim h{\to 0} \text{ } \frac{6h}{h} \rightarrow 6##

    D. ##h = 0; \frac{6h}{h} \rightarrow \text{ undefined}##
    Could you please tell me which ones are wrong?
    Thanks.
     
  5. Aug 9, 2015 #4

    Mark44

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    No.
    The limit doesn't exist. If you don't understand why, read up on left-hand and right-hand limits.
    Correct
    Correct, although it would normally be written as ##\lim_{h \to 0} \frac{6h}{3h} = 0##. In other words, without the last arrow, which indicates "approaches."

    Edit: I miswrote 0 instead of 2 as the limit. It should be ##\lim_{h \to 0} \frac{6h}{3h} = 2##
    Yes
     
    Last edited: Aug 9, 2015
  6. Aug 9, 2015 #5
    You mean ##\lim_{h \to 0} \frac{6h}{3h} = 2##?
    The "last arrow" I think is ambiguous in math.
    I should have said ##\lim_{h \to 0} \frac{6h}{3h}## is equal/match to 2.
     
  7. Aug 9, 2015 #6

    micromass

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    I want to be a bit more careful than what Mark says. Although in principle I agree with him, you seem to use arrows ##\rightarrow## everywhere, and it is not clear to me why you write this arrow. So the following are correct:

    A. ##\lim_{h\rightarrow 0} \frac{6}{h}## is undefined.
    B. If ##h=0##, then ##\frac{6}{h}## is undefined.
    C. ##\lim_{h\rightarrow 0}\frac{6h}{h} = 6##.
    D. If ##h=0##, then ##\frac{6h}{h}## is undefined.
     
  8. Aug 9, 2015 #7

    micromass

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    Yes.

    It's not ambiguous, it's just wrong to use it in that context.
     
  9. Aug 9, 2015 #8
    I should have asked directly to Mark44, but your post is the last one.
    Actually this
    doesn't have anything to do with "left-hand and right-hand limits", because it's the last arrow that I put wrongly? I just read left-hand, right-hand arrow, http://www.millersville.edu/~bikenaga/calculus/limlr/limlr.html [Broken]
    but it doesn't explain why there's no limit.
     
    Last edited by a moderator: May 7, 2017
  10. Aug 9, 2015 #9

    micromass

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    The point of the left-hand and right-hand limits is the following:
    While
    [tex]\lim_{h\rightarrow 0} \frac{6}{h}[/tex]
    is undefined. It is true that the left-hand limit
    [tex]\lim_{h\rightarrow 0-} \frac{6}{h} = -\infty[/tex]
    and the right-hand limit is
    [tex]\lim_{h\rightarrow 0+}\frac{6}{h} = +\infty[/tex]
     
  11. Aug 9, 2015 #10
    Ahh, so if the left hand and the right hand lmits differs very big, than we can say "There is no limit"?
    [Add: differ is the wrong word I think. So, the left-hand and the right-hand limit must match/exact?]
    [Add: ##\lim_{h \to 0+} \frac{6h}{h}## is equal to ##\lim_{h \to 0-} \frac{6h}{h}##, so we can say that there is a "limit" there?]
     
  12. Aug 9, 2015 #11

    micromass

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    Yes. A limit exists if and only if the left-hand and right-hand limits exist and are equal.
     
  13. Aug 9, 2015 #12
    Thanks! A new concept. This helps me much in understanding math (at least about this "limit" thing :smile:. Left hand should match right hand)
     
  14. Aug 9, 2015 #13

    HallsofIvy

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    Part of the problem is that you are trying to interpret "infinity" as if it were a number- it isn't. Saying that a limit "is equal to infinity" is the the same as saying the limit "does not exist", just in a particular way.
     
  15. Aug 9, 2015 #14

    Mark44

    Staff: Mentor

    Yes, that's what I should have written. I have edited my earlier post to indicate this.
     
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