I would like to explain in my paper that there is no upper bound for the function $f(x)$. Is there a simple notation to explain this fact?
At first, I employed $f(x)< \infty$. However, since any real number is less than $\infty$, I think this formula is meaningless. (I mean if $g(x) = \sin(x)$, $g(x) < \infty$, but, $g(x)$ is bounded by 1.)
Next, I thought of using $f(x)\leq\infty$. However, there is no real number equal to $\infty$. So I don't think it means that there is no upper bound.
Best Answer
$\sup_{x\in X}f(x)=\infty$ seems right, though you could say that $f$ is unbounded above.