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: Showing that two intervals have the same cardinality ?

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to show that [0,1] and [0,2] have the same cardinality by giving a formula for a function that is bijective. Aren't there a number of functions that can fit this description? Can I then use any one? I'm a little confused, my teacher didn't really elaborate much upon this. Is there a specific formula to find the function, not only in this case, but generally?


    Edit: I have used y=f(x)=2x, I'm guessing this process is pretty systematic when dealing with such intervals?
     
    Last edited: Jan 16, 2012
  2. jcsd
  3. Jan 16, 2012 #2

    Curious3141

    User Avatar
    Homework Helper

    You can use any bijection. f(x) = 2x is fine. So is a non-linear one like f(x) = x(3-x), which is bijective over [0,1]. It's your choice. But the former has the advantage of being immediately and intuitively obvious.
     
  4. Jan 16, 2012 #3
    There's definitely no "formula" here. Intuition and experience are your best friends when seeking for Bijections.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook