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Number must be zero

  1. Nov 12, 2015 #1
    Let N be any number
    N÷∞=0
    Cross multiplying
    N=0*∞
    Any number multiplied by zero is zero
    Even infinity is a number but it is large
    So
    N = 0
     
  2. jcsd
  3. Nov 12, 2015 #2
    Is my assumption correct
     
  4. Nov 12, 2015 #3

    DaveC426913

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    Gold Member

    No.

    You cannot perform arithmetic operations on infinity.

    More particularly, N÷∞= undefined.
     
  5. Nov 12, 2015 #4

    DrClaude

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    Staff: Mentor

    Infinity is not a number. You can't use it like that.
    $$
    \lim_{x \rightarrow \infty} \frac{N}{x} = 0
    $$
    ##
    \lim_{x \rightarrow \infty} 0 \times x
    ## is undefined.


    Correction: ##0 \times \infty## is undefined.
     
    Last edited: Nov 12, 2015
  6. Nov 12, 2015 #5

    fresh_42

    Staff: Mentor

    You assume that you can handle zero and infinity as numbers. As been said infinity isn't a number. 0 is a number but it doesn't belong to the halfgroup of ℕ or ℤ or group of ℚ or ℝ or ℂ with multiplication as group operation. It simply does not exist in there and therefore cannot be multiplicatively inverted.
     
    Last edited: Nov 12, 2015
  7. Nov 12, 2015 #6

    jbriggs444

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    Science Advisor

    [Edit: removed quote of Dr. Claude's original]

    ##
    \lim_{x \rightarrow \infty} 0 \times x
    ## is defined and is equal to zero. However, that does not mean that ##0 \times \infty## is defined.
     
    Last edited: Nov 12, 2015
  8. Nov 12, 2015 #7

    DrClaude

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    Staff: Mentor

    Yes. That was botched cut and paste. Thanks.
     
  9. Nov 12, 2015 #8
    Infinity and the infinitesimal cannot be treated as straight up values for arithmetic operations, infinity is not a number you can reach. Defined by the limit as values for x gets bigger and bigger in contrast with constants in the expression. Just like what DrClaude said.
     
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