Cardinality properties

From CS2800 wiki

Note that it is dangerous to redefine symbols like ≤ and ≥! People expect that these relations work the same way they do for numbers, but it is not a-priori obvious that they do. For example, you might expect that

Luckily, these are all true (most will be proved on the homework), but it's important to note that they need to be proved!

The last of these claims is called the Cantor-Schroeder-Bernstein theorem; the proof is much more difficult than the others.