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Math Help - meanless question

  1. #1
    Newbie sonymd23's Avatar
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    meanless question

    0 / 8 = 0

    but how come 8 / 0 = error or E.......???
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by sonymd23
    0 / 8 = 0

    but how come 8 / 0 = error or E.......???
    Let's do an example...
    \frac{16}{8}=2\text{ because }8+8=8\times2=16

    now try zero...

    \frac{8}{0}=\infty\text{ because }0+0+0+0....=0\times\infty\neq8

    so zero goes into eight infinite times, which we call undefined.

    ~ Q\!u\!i\!c\!k
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    Quote Originally Posted by sonymd23
    0 / 8 = 0

    but how come 8 / 0 = error or E.......???
    Because division by zero, is not allowed in math.
    Why?
    -----
    1)The embarassing physics answer because when one number is divided into another number that says how many times a number goes into that number. For example, 4/2 = 2 because 2 goes in 2 times.
    However, when you have 8/0 note that no matter how many times you add 0 you get thus thus you never reach 8 thus there is no such number.

    2)The improved applied mathematicians answer because when we write 10/2=5 we mean that 2 times 5 is 10, by definition of what division is (opposite of multiplication). Now when you have 0/8 the answer is 0 because 0 times 8 is 0, good. But what about 8/0? We are trying to find a number such when mutiplied by 0 results in 8, but any number multiplied by 0 is 0 how can we ever get 8!!! Futhermore, then what is the answer to 0/0? Do we say it is any number cuz any number times zero is zero, according to this definition.

    3)The elegant and perfect pure mathematicians answer I am not going to state it (I have before on this forum) because you would not understand so there would be no purpose. All, I can say when we limit divison for non-zero number we preserve a very important property called divisors of zero. Thus, to preserve this property we limit ourselves.
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    Forum Admin topsquark's Avatar
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    Actually, to be honest, the Physics answer is that is can't be done on a calculator.

    -Dan
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  5. #5
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    Quote Originally Posted by sonymd23
    0 / 8 = 0
    but how come 8 / 0 = error or E.......???
    Hello, sonymd23,

    your question isn't meaningless at all - and very difficult to answer.

    Let us assume that the division by zero is allowed. Then you can say that
    \frac{4}{4}=\frac{8}{8}=\frac{-1}{-1}=\frac{0}{0}=1

    5\ \cdot \ 0=0. Divide both sides of the equation by zero and you'll get:

    \frac{5\ \cdot \ 0}{0}=\frac{0}{0}. According to our assumption the result is:
    5 * 1 = 1

    So you see that numbers are ambiguous, if you allow the division by zero.

    (One effect of this result is: You can buy the most expensive car for 1 $, because 245,456.99 $ or 1 $, it's the same)

    Greetings

    EB
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  6. #6
    MHF Contributor Quick's Avatar
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    PH's second point

    Quote Originally Posted by sonymd23
    0 / 8 = 0

    but how come 8 / 0 = error or E.......???
    Try writing it out in an equation, such as...
    \frac{5}{0}=x

    multiply both sides by 0 5=x\times0

    solve: 5=0 as you can see this is incorrect. In fact the method to do this problem is incorrect because \frac{0}{0}=\infty

    let's try it now, with this new information:

    \frac{5}{0}=x

    multiply both sides by 0 \frac{5\times 0}{0}=x\times0

    extend: 5\frac{0}{0}=0

    solve: 5\infty=0

    this way doesn't work either! because 5 times infinity equals infinity, not zero. So as you can see, there is no mathematical way to express \frac{x}{0}
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    Quote Originally Posted by Quick
    Try writing it out in an equation, such as...
    \frac{5}{0}=x

    multiply both sides by 0 5=x\times0

    solve: 5=0 as you can see this is incorrect. In fact the method to do this problem is incorrect because \frac{0}{0}=\infty

    let's try it now, with this new information:

    \frac{5}{0}=x

    multiply both sides by 0 \frac{5\times 0}{0}=x\times0

    extend: 5\frac{0}{0}=0

    solve: 5\infty=0

    this way doesn't work either! because 5 times infinity equals infinity, not zero. So as you can see, there is no mathematical way to express \frac{x}{0}
    If anyone did such a calculation in front of me.... let me stop there.

    Never, have I seen such an informal argument.
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  8. #8
    MHF Contributor Quick's Avatar
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    Talking

    Quote Originally Posted by ThePerfectHacker
    If anyone did such a calculation in front of me.... let me stop there.

    Never, have I seen such an informal argument.
    here's an even more informal argument:
    Quote Originally Posted by Attempting to Annoy Hacker
    you can't divide by zero because someone out there says so.
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  9. #9
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    Quote Originally Posted by High School Teacher
    you can't divide by zero because someone out there says so.
    When I was younger that bothered me too. Because, I never knew the real reason why. But when I started doing formal math and seeing how the numbers and everything was constructed I finally understood and these things never bothered me ever since. For now put faith into mathematicians and try not to find what 0/0 is, because you will not. Same thing as saying, do not try to find a/b=\sqrt{2} because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.
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  10. #10
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by ThePerfectHacker
    Same thing as saying, do not try to find a/b=\sqrt{2} because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.
    It's not that I don't have faith in mathematicians, it's that the easiest way for me to remember things is to know why they are.
    also, I assume you mean that a and b have to be rational numbers.
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  11. #11
    Grand Panjandrum
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    Quote Originally Posted by Quick
    Quote Originally Posted by ThePerfectHacker
    Same thing as saying, do not try to find a/b=\sqrt{2} because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.
    It's not that I don't have faith in mathematicians, it's that the easiest way for me to remember things is to know why they are.
    also, I assume you mean that a and b have to be rational numbers.
    There are no such integers is sufficient, that there are no such rationals
    is implied by there being no such integers.

    RonL
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