Two sets are said to have the same cardinality if there exists a bijection between them. Your second function is not a bijection.

I'm new to this forum, so please excuse any improprieties. Spirituality is a curious word. It suggests an approach to ontology. On another front it invites an escape from being. Kierkegaard's leap of faith was existentially spiritual. Badiou invites fidelity to events based on a mathematical ontology. Spirituality might not be a unique category, but it's not empty, and intersects with existing categories.