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Homework Help: What's 1^infinity?

  1. Nov 10, 2013 #1
    1. The problem statement, all variables and given/known data
    What's 1^infinity?

    2. Relevant equations
    I think the answer is 1 because 1 to the power of anything equals 1, am I right? What's the answer to this?

    3. The attempt at a solution
  2. jcsd
  3. Nov 10, 2013 #2


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    Gold Member

    Yes, you are right, although I don't think it's a particularly meaningful question because it treats infinity as a number which is often not really appropriate.
  4. Nov 10, 2013 #3
    You can prove it equals 1 through calculus, but it is actually undefined because infinity isn't a real number.
  5. Nov 10, 2013 #4


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    Science Advisor
    Homework Helper

    That notation is usually shorthand for a limit a^b where a approaches 1 and b approaches infinity. If a is exactly 1, then yes, the limit is 1. Otherwise it's indeterminant (it could be anything) and the limit depends on the exact behavior of a and b.
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