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Why does dividing a number by zero not result in a value of zero? Watch

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    (Original post by hamza772000)
    So what'd be the answer?
    There is no answer.
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    (Original post by hamza772000)
    So what'd be the answer?

    Typical Asian parent mindset
    Well, guess what.... I AM ASIAN!!! (Bengali)
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    (Original post by Plagioclase)
    Not a mathematician but I'd have thought that's a perfectly reasonable explanation. Maths is simply the result of a series of axioms that we decide on because of their use in achieving sensible results. If x/0 had any defined value, it would result in logical inconsistencies.
    So that answer in your opinion is correct?
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    (Original post by B_9710)
    There is no answer.
    So I should just leave it blank? :lol: It's AS level Computing homework
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    (Original post by hamza772000)
    So that answer in your opinion is correct?
    If your answer is to ensure logical consistency then yeah, I guess so.
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    (Original post by Plagioclase)
    If your answer is to ensure logical consistency then yeah, I guess so.
    Yeah, I really don't need to o in depth anyways, thanks for your help I'll confirm with a friend tomorrow
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    (Original post by Plagioclase)
    If x is a real number and you define it being divided by zero as zero:

    \frac{x}{0} = 0
     x = 0

    Therefore it's inconsistent with the normal rules of arithmetic, that's why the value of \frac{x}{0} is undefined.
    Why can't we do what they do with complex numbers and call it a 'second zero' or 'zero negative' or another appropriate name? The demonstration below describes how there is a kind of zero or absence derived from the calculation.
    (Original post by ConicalFlask)
    I always thought of it in primary school terms.
    If there are 6 sweets, and two people want them, they get three each.
    If there are 6 sweets and no one wants them, then you can't say how many each person gets, because there are none, but you can't say they get no sweets each, because then the original 6 won't be given to anyone.
    That makes less sense than I thought, but oh well.
    If division is the equal distribution of finite objects to a finite group then the distribution is zero in the case that there is no group. Why not just make an exception to the rules of arithmetic?
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    Why would it, you can take 0 out of any real number an infinite number of times. Also dividing a number by zero does not equal infinity, or else you can prove absurd results like 2=0, it's clearly a nonsense operation.
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    (Original post by hamza772000)
    Is it because zero has no value? or because it isn't divisible? or because anything multiplied by it equals zero?(I know that doesn't sound like the right answer) or because it is not consistent with division by other numbers?

    Thanks in advance
    It doesn't equal zero because as the denominator approaches 0, the result shoots to infinity.

    \frac{1}{10}=0.1
    \frac{1}{1}=1
    \frac{1}{0.1}=10
    \frac{1}{0.01}=100
    \frac{1}{0.001}=1000

    ...and so on. As you can see, as you get closer and closer to 0 in the denominator the result goes up and up, so division by zero (even if it was possible) wouldn't be equal to 0 itself anyhow.
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    An interesting video on the subject (and other issues with 0):

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    The correct answer isn't infinity, it's actually undefined.

    When you consider x/0 = y --> x = 0*y --> x = 0 so x cannot be any number but 0 (e.g 24/0 = y --> 24 = 0*y = 0 which is a contradiction). Also note that y can be any number at all so you can't give an answer for 0/0 either.

    This wikipedia page has a pretty good explanation, there's also a graph of 1/x which shows how you can never reach 0 on the x-axis and y just tends to positive and negative infinity near 0.
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    (Original post by Jizzy Jihad)
    Why would it, you can take 0 out of any real number an infinite number of times. Also dividing a number by zero does not equal infinity, or else you can prove absurd results like 2=0, it's clearly a nonsense operation.
    Yeah, but that won't have anything to do with it, for example if I were able to take an infinite number of 2's out of a number, that doesn't necessarily mean dividing that by 2 won't result in a value of 2, no?
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    (Original post by RDKGames)
    It doesn't equal zero because as the denominator approaches 0, the result shoots to infinity.

    \frac{1}{10}=0.1
    \frac{1}{1}=1
    \frac{1}{0.1}=10
    \frac{1}{0.01}=100
    \frac{1}{0.001}=1000

    ...and so on. As you can see, as you get closer and closer to 0 in the denominator the result goes up and up, so division by zero (even if it was possible) wouldn't be equal to 0 itself anyhow.
    YESS! Thanks, makes sense now
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    You just can't divide a number by zero.

    In fields, that is systems of mathematical objects, defined by certain rules, we can perform addition and multiplication. We have things called "inverses". Every field has an identity element, 1, and a zero element 0. Basically, multiplying by 1 does nothing, and adding 0 does nothing. Every non-zero element in the field has an inverse, i.e. for every "a" in the field there is a "b" such that ab = ba = 1. But 0 does not have an inverse.

    An example of a field is the real numbers. When we "divide" real numbers together, we are really finding an inverse, then applying multiplication. Division is not its own thing, it is a shorthand for this process. x/y means find the inverse of y, then multiply x by that inverse. With 0, we fail at the first hurdle, as 0 does not have an inverse. There is no number, x for instance, such that 0 * x = 1. Division by 0 cannot be done. It is undefined.

    Of course, we don't have to look at things through the field lens. But it's how this stuff is rigorously supported, so I think it's pertinent. Others have already stated more number-orientated intuitive ways of looking at this.
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    (Original post by Mistletoe)
    If division is the equal distribution of finite objects to a finite group then the distribution is zero in the case that there is no group. Why not just make an exception to the rules of arithmetic?
    I always thought of it more like trying to put the 6 sweets into 0 groups - you can't do it because putting 0 in a group still leaves 6 sweets left that need to be sorted.
    It works for explaining it to kids anyway
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    (Original post by Mistletoe)
    Why can't we do what they do with complex numbers and call it a 'second zero' or 'zero negative' or another appropriate name? The demonstration below describes how there is a kind of zero or absence derived from the calculation.

    If division is the equal distribution of finite objects to a finite group then the distribution is zero in the case that there is no group. Why not just make an exception to the rules of arithmetic?
    Well, that's pretty much precisely what we do. We give it the characteristic of being "undefined". If you want to consider that as a "second zero" then you can, it's just a name which means it has no value that has any meaning in mathematics. Unlike complex objects, I do not think the undefined object is logically useful in anyway. I also do not agree that the demonstration suggests the value is "kind of zero".
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    (Original post by hamza772000)
    YESS! Thanks, makes sense now
    Good.

    Also in regard to division by 0 equaling infinity; nope. Infinity is not a number therefore we cannot define division by 0 to be equal to it, therefore division by 0 is undefined.

    If you have 0/0 then you might think that it either shoots up to infinity, or it simply equal to 1 because its a number divided by itself. For this reason, we cannot determine which one it is therefore this result is indeterminate.
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    (Original post by hamza772000)
    Yeah, but that won't have anything to do with it, for example if I were able to take an infinite number of 2's out of a number, that doesn't necessarily mean dividing that by 2 won't result in a value of 2, no?
    Which number can you take an infinite number of twos out of? :rofl: If I have a number which gives me magical powers, why am I not a wizard?


    Because it's something I made up rather than an actual mathematical object.
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    (Original post by RDKGames)
    Good.

    Also in regard to division by 0 equaling infinity; nope. Infinity is not a number therefore we cannot define division by 0 to be equal to it, therefore division by 0 is undefined.

    If you have 0/0 then you might think that it either shoots up to infinity, or it simply equal to 1 because its a number divided by itself. For this reason, we cannot determine which one it is therefore it is indeterminate.
    Yeah, I know, it's just the fact that as we keep getting closer to zero the numbers start shooting up and gets too high before it actually reaches zero, right?

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    (Original post by Jizzy Jihad)
    Which number can you take an infinite number of twos out of? :rofl: If I have a number which gives me magical powers, why am I not a wizard?


    Because it's something I made up rather than an actual mathematical object.
    I was just trying to give an example Flopped. :lol:

    Ok
 
 
 
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