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Math Help - Is 1 equal to 0?

  1. #1
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    Is 1 equal to 0?

    I found this in some other website, its basically the manipulation of a formula to finally give 1=0!. Here it is:

    Let x = 1
    Then, x^2=x
    x^2-1 = x-1
    Dividing both sides by (x-1), we get
    x+1 = 1
    x+1-1 = 0, so
    Since x=1,
    1=0

    Any explanations?
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  2. #2
    Super Member Quacky's Avatar
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    Re: Is 1 equal to 0?

    Quote Originally Posted by IBstudent View Post
    I found this in some other website, its basically the manipulation of a formula to finally give 1=0!. Here it is:

    Let x = 1
    Then, x2=x
    x2-1 = x-1
    Dividing both sides by (x-1), we get
    x+1 = 1
    x+1-1 = 0, so
    Since x=1,
    1=0

    Any explanations?
    This is very old.
    "x = 1"
    "Dividing both sides by (x-1)"
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  3. #3
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    Re: Is 1 equal to 0?

    Quote Originally Posted by IBstudent View Post
    I found this in some other website, its basically the manipulation of a formula to finally give 1=0!. Here it is:

    Let x = 1
    Then, x^2=x
    x^2-1 = x-1
    Dividing both sides by (x-1), we get <--- here you divide by zero which isn't allowed
    x+1 = 1
    x+1-1 = 0, so
    Since x=1,
    1=0

    Any explanations?
    ...
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  4. #4
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    Re: Is 1 equal to 0?

    You are correct that \displaystyle 1 = 0!, but \displaystyle 1 \neq 0.

    \displaystyle \begin{align*} n! &= n(n - 1)! \\ \frac{n!}{n} &= (n - 1)! \end{align*}

    Now letting \displaystyle n = 1 we have

    \displaystyle \begin{align*} (1-1)! &= \frac{1!}{1} \\ 0! &= \frac{1}{1} \\ 0! &= 1 \end{align*}
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  5. #5
    Super Member Quacky's Avatar
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    Re: Is 1 equal to 0?

    Quote Originally Posted by Prove It View Post
    You are correct that \displaystyle 1 = 0!, but \displaystyle 1 \neq 0.

    \displaystyle \begin{align*} n! &= n(n - 1)! \\ \frac{n!}{n} &= (n - 1)! \end{align*}

    Now letting \displaystyle n = 1 we have

    \displaystyle \begin{align*} (1-1)! &= \frac{1!}{1} \\ 0! &= \frac{1}{1} \\ 0! &= 1 \end{align*}
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  6. #6
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    Re: Is 1 equal to 0?


    \boxed{\begin{array}{c}\text{Theorem} \\[2mm]1 = 0\:\text{ for large values of }0.\end{array}}

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