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 $x$?

  • $\begingroup$ 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 $n$? $\endgroup$ Oct 12, 2021 at 22:44
  • $\begingroup$ 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. $\endgroup$ Oct 12, 2021 at 22:44
  • $\begingroup$ @TheoBendit that's precisely what I'm looking for. $\endgroup$ Oct 12, 2021 at 22:51
  • $\begingroup$ @ThomasAndrews my apologies; I'm not familiar with it, and as such am trying to learn. $\endgroup$ Oct 12, 2021 at 22:52
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    $\begingroup$ @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. $\endgroup$ Oct 12, 2021 at 23:15


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