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    Thread: Divide by Zero

    1. #1
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      Divide by Zero

      Okay.

      So dividing by zero makes no sense.

      r * 24 = 0

      24/0 = 0

      r = 0

      0 * 24 = 0

      Thus, is true?

      I get what I've heard for some explanations, but that's just weak.

      I want a technical explanation :3

      EDIT:

      I got 24/0 = 0 like this....:

      If you split 24 up into 0 groups (i.e. take it away), then you are left with nothing.
      Last edited by A Roxxor; 09-30-2008 at 12:59 AM.

    2. #2
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      24 / 0 is undefined, not zero

      Why is this in tech forum?

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      Yea, I've heard.

      That isn't an explanation.

    4. #4
      FBI agent Ynot's Avatar
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      what exactly are you asking?
      (\_ _/)
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      SPECIFICALLY, why is x/0 'undefined'?

      Not, "Because it is undefined".

    6. #6
      DuB
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      The mistake you are making is assuming that splitting 24 into 0 groups is theoretically equivalent to "taking it away." Taking the 24 away would be subtraction (24 - 24 = 0). Splitting 24 into 0 groups, on the other hand, is not possible.

    7. #7
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      Why not?

      After all, we can add 5 to itself zero times and get zero. So why wouldn't such abstractions apply here?

    8. #8
      FBI agent Ynot's Avatar
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      well, it's not undefined
      it's infinity
      machines leave a divide by zero as undefined because you can't represent it

      Division is the ratio between 2 numbers
      R = a / b

      12 / 4 = 3
      3 = 12 / 4

      the ratio between 4 & 12 is 3
      put simply, 12 is 3 times larger than 4

      for ever decreasing values of b, the ratio increases

      12 / 4 = 3

      12 / 1 = 12

      12 / 0.1 = 120

      12 / 0.01 = 1200

      12 / 0.000000001 = 12000000000

      the closer the denominator gets to zero, the larger the result
      if the denominator is zero, the result is infinitely large
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    9. #9
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      Okay, I see. Thank you.

      But then, it isn't undefined, it is ifinity, so why doesn't it work? Infinity is represented as 'infinity'.

      Any operation on it results in itself.

      But then, that doesn't work because

      r * 24 = 0

      r = inf

      inf * 24 = inf

      r HAS to be 0.
      Last edited by A Roxxor; 09-30-2008 at 01:31 AM.

    10. #10
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      Should I do it? Yeah, okay. There is a way to essentially divide by zero, it's the basis of calculus. Calculus is largely about finding inventive ways to divide by zero.

    11. #11
      Look away wendylove's Avatar
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      the closer the denominator gets to zero, the larger the result
      if the denominator is zero, the result is infinitely large
      Thats not rigor.

      Basically if you have y=1/x, as x tends to 0, y tends to infinty.

      Ironically, speaking you can actually work with that using nonstandard analysis.

      I have a book on abstract algebra, it touches this subject. It says something about this algebra shows thats why division by zero is not allowed, however I couldn't understand the book after about three pages.

      There is a way to essentially divide by zero, it's the basis of calculus. Calculus is largely about finding inventive ways to divide by zero.
      In calculus you never divide by zero, actually if you're forced to do that then you have to concluded it has no limit. In calculus you work with infintely small quantities, not zero.
      Last edited by wendylove; 09-30-2008 at 01:35 AM.
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

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      Er, not sure what you mean, Wendy...

      Ninja:

      Heh.

      My Uncle's taking a calculus course. Looks hella abstract }_}

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      FBI agent Ynot's Avatar
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      infinity is not a number
      you cannot do calculations on it

      infinity is a representation of a value so large (or small) you can't define it

      how long, in metres, is the universe?
      it just keeps going, and going

      you can fly around in a space ship all your life, placing rulers end-to-end and always need more rulers
      so, how long is it?
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    14. #14
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      Quote Originally Posted by wendylove View Post
      I have a book on abstract algebra, it touches this subject. It says something about this algebra shows thats why division by zero is not allowed, however I couldn't understand the book after about three pages.
      Algebra can not divide by zero, you can only do that through calculus. I assume what you are talking about is polynomials that have discrete breaks. That's not quiet the same as division by zero.

      Calc isn't that hard, you just have to get used to it.

      Ynot is correct, infinity is a concept, not a number.

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      Quote Originally Posted by Ynot View Post
      infinity is not a number
      you cannot do calculations on it

      infinity is a representation of a value so large (or small) you can't define it

      how long, in metres, is the universe?
      it just keeps going, and going

      you can fly around in a space ship all your life, placing rulers end-to-end and always need more rulers
      so, how long is it?
      It is still represented as infinity.

      Any operation on it results in itself.

      What I don't understand, is this.

      r * 24 = 0

      r = 0

      This is true, because 0*x = 0

      So then:

      r * 24 = 0

      r = 24/0

      r = 0

      If the previous statement is true, then why is this not true?

    16. #16
      Look away wendylove's Avatar
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      My Uncle's taking a calculus course. Looks hella abstract }_}
      Calculus can be done by blind monkies with broken fingers. Analysis is abstract, calculus is just doing a technique.

      infinity is not a number
      Do set theory and come back here saying that. Infinity is a number, Cantor said so.

      you can fly around in a space ship all your life, placing rulers end-to-end and always need more rulers
      so, how long is it?
      This means nothing, and its not rigor. Numbers are abstract, this proves nothing.
      Last edited by wendylove; 09-30-2008 at 01:40 AM.
      Xaqaria
      The planet Earth exhibits all of these properties and therefore can be considered alive and its own single organism by the scientific definition.
      7. Reproduction: The ability to produce new organisms.
      does the planet Earth reproduce, well no unless you count the moon.

    17. #17
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      Just because something can be used for mathematical functions does not make it a number. i is not a number, but i^2 is. Quaternions aren't numbers either.


      0 is a weird number in math. You can take a defined equation like the one that you mentioned, move it around and make the variable be different things

      r * 24 = 0 : r = 0
      0 / r = 24 : r = undefined
      r = 24 / 0 : r = infinity

    18. #18
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      Quote Originally Posted by ninja9578 View Post
      Just because something can be used for mathematical functions does not make it a number. i is not a number, but i^2 is. Quaternions aren't numbers either.


      0 is a weird number in math. You can take a defined equation like the one that you mentioned, move it around and make the variable be different things

      r * 24 = 0 : r = 0
      0 / r = 24 : r = undefined
      r = 24 / 0 : r = infinity
      I didn't say it was a number...

      And that makes no sense.

      In order to find that

      r * 24 = 0

      so then

      r = 0

      You would have to say

      r = 24/0

      r = 0

      So.

      And wouldn't 0/r = 24 be false anyhow?

      Take nothing, split it up, and you still have nothing.

    19. #19
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      Here's a quick lesson in calculus. Say you want the slope of a line at a single point in the line y = f(x). The calculus way to do that is rise over run, but in this case, run is zero because it's just a point.

      We need to find some way to solve for a point, so lets use the algebraic way to solve

      slope = rise / run
      f(x)' = dy / dx

      Chose any x, and add a little bit to it. We'll call that little bit ∆x. That ∆x is out run now, but remember we want that run to be zero, so the limit of ∆x is zero.

      f(x)' = lim ∆x -> 0 (dy / ∆x)

      Now lets change dy. We know that f(x) gives us y so f(x + ∆x) - f(x) will gives us dy.

      f(x)' = lim ∆x->0 (f(x + ∆x) - f(x) / ∆x)

      Now we need to know what the function f(x) is. For simplicity, lets use f(x) = x^2. So...

      f(x)' = lim ∆x->0 ((x + ∆x)^2 - x^2 / ∆x)

      Now lets simplify.

      f(x)' = lim ∆x->0(2x∆x + ∆x^2)/∆x

      Now we have a ∆x on the bottom and in each function in the top. This allows us to cancel them out. This is what calculus is all about, keeping that zero a variable as long as possible and finding a way to cancel it out. However you'll notice when we simplify, there still is a ∆x on the top because on of them is square:

      f(x)' = lim ∆x->0(2x + ∆x)

      But now the limit of ∆x is zero, so replace ∆x with zero.

      f(x)' = 2x, which is the derivative of x^2

    20. #20
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      Quote Originally Posted by A Roxxor View Post
      And wouldn't 0/r = 24 be false anyhow?

      Take nothing, split it up, and you still have nothing.
      Yes, that's why that variation of that equation is undefined.

    21. #21
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      Quote Originally Posted by A Roxxor View Post
      It is still represented as infinity.

      Any operation on it results in itself.

      What I don't understand, is this.

      r * 24 = 0

      r = 0

      This is true, because 0*x = 0

      So then:

      r * 24 = 0

      r = 24/0

      r = 0

      If the previous statement is true, then why is this not true?
      You fail MAJORLY at basic re-arranging of equations, and everyone else in this thread fails to varying degrees as well.

      r*24 = 0

      divide both sides by 24:
      r = 0/24
      r=0

      If you can't understand that then I suggest you go back and redo third grade.

      As for the undefined/infinity discussion:

      A quantity x/0, x real, is undefined. To see why, look at the left and right limits of the function y=1/x as x approaches 0. The left limit will give you -infinity, and the right limit gives +infinity. Thus, the limit does not exist, and 1/0 is undefined in the reals. It's not a rigorous proof, it just demonstrates why 1/0 is not infinity.

      I suggest you ALL read this:
      http://en.wikipedia.org/wiki/Divide_by_zero

    22. #22
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      Uhm, there are multiple ways to rearrange the same equation.

      Quote Originally Posted by ninja9578
      r * 24 = 0 : r = 0
      0 / r = 24 : r = undefined
      r = 24 / 0 : r = infinity
      All are rearrangements of the same equation

      a * b = c can be
      b = c / a or a = c / b


      FYI: This thread is moved to the lounge as this is not a discussion on implementing division by zero.

    23. #23
      Eprac Diem arby's Avatar
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      0/0 could technically be any number

      'infinity' is only commonly cited because the function 1/x approaches it from the right

      Think about this

      5*0 = 0

      5 = 0/0

      20* 0 = 0

      20 = 0/0

      135*0 = 0

      135 = 0/0

      According to the above statements, 5 = 20 = 135 which is why we say 0/0 is undefined, it equals any number.

    24. #24
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      Quote Originally Posted by drewmandan View Post
      You fail MAJORLY at basic re-arranging of equations, and everyone else in this thread fails to varying degrees as well.

      r*24 = 0

      divide both sides by 24:
      r = 0/24
      r=0

      If you can't understand that then I suggest you go back and redo third grade.

      As for the undefined/infinity discussion:

      A quantity x/0, x real, is undefined. To see why, look at the left and right limits of the function y=1/x as x approaches 0. The left limit will give you -infinity, and the right limit gives +infinity. Thus, the limit does not exist, and 1/0 is undefined in the reals. It's not a rigorous proof, it just demonstrates why 1/0 is not infinity.

      I suggest you ALL read this:
      http://en.wikipedia.org/wiki/Divide_by_zero
      ???

    25. #25
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      Quote Originally Posted by arby View Post
      0/0 could technically be any number

      'infinity' is only commonly cited because the function 1/x approaches it from the right

      Think about this

      5*0 = 0

      5 = 0/0

      20* 0 = 0

      20 = 0/0

      135*0 = 0

      135 = 0/0

      According to the above statements, 5 = 20 = 135 which is why we say 0/0 is undefined, it equals any number.
      Well yea.

      'r' could be any number in

      r*0=0

      That's the point.

      We know that.

      But, in r*x=0 (Where 'x' is any real number) then r = 0

      So then, r = x/0

      Which was my original question and has failed to have been answered.

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