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∞/2= ∞?

  1. Aug 5, 2011 #1
    ∞/2= ∞

    Please comment. I do not thnk this is right.
     
  2. jcsd
  3. Aug 5, 2011 #2

    HallsofIvy

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    What number system are you working in? Strictly speaking, in the real number system, there is no "[itex]\infty[/itex]" but you can think of that as "shorthand" for [itex]\lim_{x\to\infty} x/2[/itex]. In that case, yes, that limit is [itex]\infty[/itex].

    And, in any number system in which [itex]\infty[/itex] is defined as a number (extended reals, for example) it is true that [itex]\infty/ 2= \infty[/itex].
     
  4. Aug 5, 2011 #3
    Is there any logical or math problem with the value of ∞ in this question? Does the value of ∞ change?
     
  5. Aug 5, 2011 #4

    Mentallic

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    Why not? What would you expect a never ending number which is halved to be?
     
  6. Aug 6, 2011 #5

    Hurkyl

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    No. ∞ = ∞. Why do you think ∞/2 should have a different value from ∞?

    (my assumption for this post: we are working in the extended real numbers or projective real numbers)

    Most likely answer: you are trying to apply your intuition about algebra of real numbers. But ∞ isn't a member of the real numbers, and so it can behave differently -- and this particular algebraic behavior is one example of that different behavior.

    If you actually think about what ∞ is defined to be or what sorts of things it can quantify ∞=∞/2 should actually be rather obviously true.
     
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