What is Numerical Equivalence of Sets and How is it Defined?

[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

 

[Mark44]

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.