# Math Help - Prove equal powers (probably fairly primitive)

1. ## Prove equal powers (probably fairly primitive)

Hello.

My discrete mathematics course has just started, so I'm not very good even at probably fairly easy things:

Prove if $\displaystyle $G = A \times B$$ is a bijection between finite sets $\displaystyle $A$$ and $\displaystyle $B$$ then $\displaystyle $\left| A \right| = \left| B \right|$$.

It looks pretty obvious because of the nature of this bijection, but I just can't seem to figure out notations to prove it in a mathematical way.

Thanks.

2. A bijection is a function, but if A is nonempty and |B| > 1, then A x B is not a function. If there is no mistake in the question, then the fact that A x B is a bijection implies that |A| = |B| = 1 or |A| = |B| = 0, so |A| = |B|.