Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Definition of set R^R?

  1. Mar 2, 2008 #1
    1. The problem statement, all variables and given/known data
    What is the set R^R? Is it used to define functions and show that the function produces real solutions?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 2, 2008 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    X^Y usually denotes the set of functions from Y to X.

    But I've also seen R^R denote an R-fold Cartesian product of R.
     
  4. Mar 2, 2008 #3
    Okay, in this question after it writes R^R it says "of all functions from R to R", so i think they just mean that solutions are real?
     
  5. Mar 2, 2008 #4

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    "solutions" is not the right word, but I get what you mean.
     
  6. Mar 2, 2008 #5
    Oh sorry, i mean the function maps to a real number.
     
  7. Mar 3, 2008 #6

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Formally, R^R is indeed the set of all R-fold tuples of real numbers. That is, an element of R^R is sort of a vector, containing in each slot a real number, and having as many slots as there are real numbers.
    In everyday mathematical usage we call such an object a function from R to R.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook