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Just want to clear this up

  1. Apr 30, 2004 #1
    Is [tex]\frac {1}{\infty} = 0[/tex] , or is it just infinitely close to 0?
     
    Last edited: Apr 30, 2004
  2. jcsd
  3. Apr 30, 2004 #2

    mathman

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    = is correct, the other alternative is not too meaningful, unless you get involved with non-standard analysis.
     
  4. Apr 30, 2004 #3
    Unless you're using non-standard analysis I don't think the statement [itex]\frac{1}{\infty}=0[/itex] is even meaningful.
     
  5. Apr 30, 2004 #4

    jcsd

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    Well, you could say 1/x -> 0 as x tends to infinity (though that obviously doesn'; mean 1/inifnity = 0 especially when infinity isn't even a number).
     
  6. Apr 30, 2004 #5
    Lets say there is 1 unit of something in an infinitely large area...then would you say = ? Because then that says that the unit doesn't even exist...
     
  7. Apr 30, 2004 #6

    jcsd

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    No in that situation all we would be saying is that it would be meaningless to talk about the ratio of the area to the unit area.
     
  8. Apr 30, 2004 #7
    No it isn't...Because that unit DOES exist. But by saying 1/inf = 0...we say it is non-existant. In the same way, human population with respect to time would be 0 if the above statement were true. This is not so...
     
  9. Apr 30, 2004 #8

    Hurkyl

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    1/∞ doesn't have a "standard" meaning; in some systems where infinite numbers are defined, division doesn't exist. In some others, 1/∞ is some infinitessimal positive nonzero number. In others, 1/∞=0.

    If you're thinking of ∞ as that "big number that sits at the positive end of the real numbers", then you probably mean to use the extended real numbers, where 1/∞ is defined to be equal to zero.
     
  10. Apr 30, 2004 #9

    Integral

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    In my books when infinity is defined as an extension to the Real number line, operations on infinity are also defined, included with these definitions is:

    [tex] \frac 1 \infty = 0 [/tex]

    This is a very specific definition for a very specific application ie the real numbers. If you attempt to apply this definition out of context your results may vary.
     
  11. May 1, 2004 #10
    I always thought it meant infinitely close to zero, and that’s why the delta at the end of an integral doesn’t yield zero results, because the delta doesn’t actually = zero, just something infinitely small.
     
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