Given $M = \left\{ k \mid a _ { k } = b _ { k } \right\}$, where $a _ { n }, b _ { n }$ are not constant sequences and all terms are distinct. Which of the following is correct? \_\_\_ (1) If $a _ { n }, b _ { n }$ are both arithmetic sequences, then $M$ has at most one element; (2) If $a _ { n }, b _ { n }$ are both geometric sequences, then $M$ has at most three elements; (3) If $a _ { n }$ is an arithmetic sequence and $b _ { n }$ is a geometric sequence, then $M$ has at most three elements; (4) If $a _ { n }$ is monotonically increasing and $b _ { n }$ is monotonically decreasing, then $M$ has at most one element.
Given $M = \left\{ k \mid a _ { k } = b _ { k } \right\}$, where $a _ { n }, b _ { n }$ are not constant sequences and all terms are distinct. Which of the following is correct? \_\_\_\\
(1) If $a _ { n }, b _ { n }$ are both arithmetic sequences, then $M$ has at most one element;\\
(2) If $a _ { n }, b _ { n }$ are both geometric sequences, then $M$ has at most three elements;\\
(3) If $a _ { n }$ is an arithmetic sequence and $b _ { n }$ is a geometric sequence, then $M$ has at most three elements;\\
(4) If $a _ { n }$ is monotonically increasing and $b _ { n }$ is monotonically decreasing, then $M$ has at most one element.