# Numerical equivalence of sets

1. Feb 16, 2010

### Piglet1024

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 $$\exists$$F:X$$\rightarrow$$Y that is bijective or there are two injective functions f:X$$\rightarrow$$Y and g:Y$$\rightarrow$$X

2. Feb 16, 2010

### 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.