Just want to clear this up

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

    mathman 6,512
    Science Advisor
    Gold Member

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

    jcsd 2,226
    Science Advisor
    Gold Member

    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. 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. jcsd

    jcsd 2,226
    Science Advisor
    Gold Member

    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. 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. Hurkyl

    Hurkyl 16,090
    Staff Emeritus
    Science Advisor
    Gold Member

    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. Integral

    Integral 7,345
    Staff Emeritus
    Science Advisor
    Gold Member

    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. 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.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?