[Aurelius]

Your statement is true - but the emphasis is on one-to-oneness (bijectivity is a somewhat less awkward technical equivalent). The fundamental notion being that two sets, infinite or not, have the same cardinality if, and only if, there is a one-to-one correspondance between them. So, the interest is in one-to-one correspondences. I hope that I interpreted your question correctly and have answered it.

[Faraday]

Thanks for your comments on #196.