The following exercise gives me headaches:
Show: If the polynomial hierarchy is strict (i.e. $\forall k \in \mathbb{N}. \Sigma_k \neq \Sigma_{k+1}$), then there is no $\text{PH}$-complete problem for polynomial-time reductions (i.e. there is no problem $\text{P} \in \text{PH}$ such that each problem in $\text{PH}$ can be reduced to $\text{P}$ through a function $f \in \text{FP}$).
The exercise describes in detail what has to be shown, but my issue is that I don't know how to show this. Can somebody please help me?