How do I write that $f(n)$ should equal $x$?

Let's say I create a function $$f(n) = 3n - 1$$; how can I later write that the function $$f(n)$$ should be equal to some value $$x$$? My research is telling me this is written as $$f(n) \equiv x$$ which says that $$f(n)$$ is equivalent to $$x$$. However, is this misleading in any way? It seems that "equal by definition" would be a better fit here writing it as $$f(n) := x$$ or $$f(n) ≜ x$$.

How do I write that the result of a function $$f(n)$$ should equal some value $$x$$?

• Saying $f(n) \equiv x$ says to me that $f$ is the constant function with value $x$, i.e. $f(n) = x$ for all $n$. This is obviously misleading if $f(n) = 3n - 1$, as $f$ is not a constant function in this case. I'm not really certain what you are actually asking here. Are you looking for a symbolic way of saying $f(n)$ should attain the value $x$ for some $n$? Oct 12, 2021 at 22:44
• Wait, so $3n+1$ isn’t the definition of $f(n)?$ You need to be more specific here about things. $:=$ is used for defining a function. Oct 12, 2021 at 22:44
• @TheoBendit that's precisely what I'm looking for. Oct 12, 2021 at 22:51
• @ThomasAndrews my apologies; I'm not familiar with it, and as such am trying to learn. Oct 12, 2021 at 22:52
• @Yorch It's another way of writing "defined to be", much like $:=$. It doesn't seem to be particularly popular in my experience, but I have seen it before. Oct 12, 2021 at 23:15