Definition. A cardinal is an ordinal which it is not in bijection with any smaller ordinal.
Notation. $|X|$ means that cardinal of $X$.
Proposition 1. Let $w$ be an ordinal. Then $|w+1|=w.$
Proposition 2. $|w^2|=w$.
I couldn't understand proposition 1 and 2, can you explain that why $|w+1|=w$ and $|w^2|=w$.