"$g(x)$ is greater than or equal to $0.5$ for some $x$" is equivalent to "$g(x)$ is not less than $0.5$ for all $x$".
In mathematical symbols, the former translates to "$g(x) \geq 0.5$ for some $x$". I'm confused about the latter. Should it be "$g(x) \not≮0.5$ for all $x$"? When I speak aloud it sounds correct as I am saying the whole thing as "not less than for all $x$". But then I'm thinking that $\not<$ and $\geq$ are the same thing and the statement is really saying that "$g(x) \geq 0.5$ for all $x$" which is not true.