# Thread: Exists Bijection to a Disjoint Set

1. Originally Posted by MoeBlee
Note that we could just as well have used domain rather than range.

dom(E) = {x | exists a y such that <x y> in E}.

Let z not in dom(E).

So E is disjoint from {z} X F.

And F is 1-1 with {z} X F.
In fact you don't even need to do that. In fact I prefer to use just X or something so as to avoid the misleading language of mapping / relation theory.

See what I did in:

Exists Bijection to a Disjoint Set - ProofWiki

2. I don't know what you think is "misleading" about "mapping/relation theory". For that matter, I don't know what you mean by "mapping/relation theory" that is not just part of basic set theory.