Hi, the question posed to me is as follows:

Prove or find a counterexample to:

1.$\displaystyle \alpha\cup\{\alpha \}$ is an ordinal $\displaystyle \Rightarrow \alpha$ is an ordinal

2.$\displaystyle \alpha\cup\bigcup{\alpha}$ is an ordinal $\displaystyle \Longleftrightarrow \alpha$ is an ordinal

I've found proofs to both of these questions but I'm not entirely sure that they are both correct. Can anyone see a way these implications do not hold?

Thank you.