Suppose $(a_1,\dots,a_n)$ is a sequence of real numbers such that $$a_1\leq a_2\leq \dots \leq a_n.$$
If $(b_1,\dots b_n)$ is a rearrangement of the sequence $(a_1,\dots,a_n)$ such that $$b_1\leq b_2\leq \dots \leq b_n,$$ then does it follow $a_1=b_1,\dots,a_n=b_n$?
I know that if the sequences were strictly monotonic, then the conclusion would have been obvious. How do I prove the question here, though... please help me with a proof maybe. Thank you in advance.