TITLE: Can I say that a fixed constant is less or equal infinity?
QUESTION [3 upvotes]: Mathematically speaking, given $c\in\mathbb{R}$, can I say that: $c\leq\infty$?
E.g., is $10 \leq \infty$ a correct mathematical statement?
I know this comparison is true in computer arithmetic, however is it correct from mathematical point of view? Does the "equality" part in $\leq$ matter here?

REPLY [0 votes]: Sure. An example where this is used in mathematics is when talking about $L^p$-spaces. The only thing you need to know about these is that they depend on a real parameter $p$ which is allowed to take the value $\infty$, and it's common to make statements about $L^p$-spaces which are uniform in the parameter $p$, e.g. to say "for all $1 \le p \le \infty$, the $L^p$-space satisfies..."
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