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: Numerical equivalence of sets

  1. Feb 16, 2010 #1
    1. Define numerical equivalence of sets



    2. I'm not sure how in depth the definition needs to be, how is my current def?



    3. X is numerically equivalent to Y if [tex]\exists[/tex]F:X[tex]\rightarrow[/tex]Y that is bijective or there are two injective functions f:X[tex]\rightarrow[/tex]Y and g:Y[tex]\rightarrow[/tex]X
     
  2. jcsd
  3. Feb 16, 2010 #2

    Mark44

    Staff: Mentor

    Seems reasonable. I haven't seen the term "numerical equivalence" used. What I have seen is "same cardinality." I don't think you need to have two injective functions; just one bijective function should do the job.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook