How to write in mathematical symbols the expression "range over"

Question

My question is really simple, how can I write symbolically this phrase:

$x=\sum a_mx^m$ where $m$ range over $\{1,\ldots,g\}\setminus\{t_1,\ldots,t_u\}$

Being more specific, I would like to know how to write with mathematical symbols this part: "range over $\{1,\ldots,g\}\setminus\{t_1,\ldots,t_u\}$"

Thanks

Answer 1

Often we see something like$$x=\sum_{m\in\{1,\ldots,g\}\setminus\{t_1,\ldots,t_u\}} a_mx^m$$

Answer 2

I'd suggest $$\Large x=\sum_{\substack{m=1\\[0.1cm] m\,\notin\, \{t_1,\,\ldots\,,\,t_u\}}}^g a_mx^m$$