P-adic Norm and Absolute Value are Not Equivalent

Theorem
Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the rationals $\Q$ for some prime number $p$.

Let $\size{\,\cdot\,}$ be the absolute value on the rationals $\Q$.

Then $\norm {\,\cdot\,}_p$ and $\size{\,\cdot\,}$ are not equivalent norms.

That is, the topology induced by $\norm {\,\cdot\,}_p$ does not equal the topology induced by $\size {\,\cdot\,}$.