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Math Help - Zero as number like all the others

  1. #1
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    Zero as number like all the others

    I dont know if this is the right place to place this question. The other day i started thinking a lot about this, and it just won't get out of my mind. Why does zero has the properties of any other number? Maybe the question should be, "why shouldn't it?"
    1+1+1 = 3x1

    n x n = n^2

    n( n+1)= n^2 + n

    why can N be replaced by 0 and all properties still hold?

    why does 3*0 = 0, and 0*0*0=0^3 and still its the same as 0?

    why does zero has properties like N x 0 =0 for any N

    i can't even explain my question in good terms, its just a brainwashing of non-intuition on my mind, which i cannot get rid of, and its destroying my intuitions. Can someone help me believing again that 0 is a number like any other??

    Thanks in advance
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  2. #2
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    Re: Zero as number like all the others

    I really don't understand your question. 0 is a number like all others and, like all other numbers, it is "unique"- it has some properties that other numbers do not. Yes, 0 times any number is 0, just as 2 times any number is even.

    Abstractly, that property comes from the fact that 0 is the "additive identity" (x+ 0= x for any number) and the distributive law (a(b+ c)= ab+ bc).

    x(y+ 0)= xy+ x0, by the distributive law.
    x(y+ 0)= xy since 0 is the additive identity. Since xy+x0= x(y+ 0)= xy, we have xy+ x0= xy and, subtracting xy from both sides, x0= 0.
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  3. #3
    Grand Panjandrum
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    Re: Zero as number like all the others

    Quote Originally Posted by DarkFalz View Post
    I dont know if this is the right place to place this question. The other day i started thinking a lot about this, and it just won't get out of my mind. Why does zero has the properties of any other number? Maybe the question should be, "why shouldn't it?"
    1+1+1 = 3x1

    n x n = n^2

    n( n+1)= n^2 + n

    why can N be replaced by 0 and all properties still hold?

    why does 3*0 = 0, and 0*0*0=0^3 and still its the same as 0?

    why does zero has properties like N x 0 =0 for any N

    i can't even explain my question in good terms, its just a brainwashing of non-intuition on my mind, which i cannot get rid of, and its destroying my intuitions. Can someone help me believing again that 0 is a number like any other??

    Thanks in advance
    If on three consecutive days I give you zero apples, how many apples do you have?

    (I assume you haven't eaten or given away any)

    CB
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  4. #4
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    Re: Zero as number like all the others

    The thing is that i made the mistake of thinking too much about things. But zero also behaves the way it should in nature. F=m*a which means that for each mass unit we have 1 unit of "a" acceleration to equal the force. With 0 mass we have 0 force cuz we have 0*a acceleration units. Its just that it fits so well in everything. But what messes me the most, is things like this 0( 0+1) = 0*0 + 0*1 and still it all reduces to 0. Zero absorbs an complex formula, such that 0( A COMPLEX FORMULA) =0
    its such a powerful concept
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  5. #5
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    Re: Zero as number like all the others

    The thing is, 0 also behaves as expected with nature, F=m*a works even for m=0 or a=0. Is it that 0 is so much connected to nature that it perfectly resembles it?
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