Read the statements carefully.

$[1]$. If $f(x)<g(x)$ for all $x$, then $\displaystyle \lim_{x\to c} f(x) < \displaystyle \lim_{x\to c} g(x)$ provided that these limits exist.

$[2]$. If both $\displaystyle \lim_{x\to c} f(x)$ and $\displaystyle \lim_{x\to c} g(x)$ do not exist, then it is impossible for $\displaystyle \lim_{x\to c} (f(x)+g(x))$ to exist.

$[3]$. If $\displaystyle \lim_{x\to c} f(x)=l$ and $\displaystyle \lim_{x\to c} f(x)=m$, then $l$ is always equal to $m$.

Which of these are true?