# Formal notation for function equality

Is there a short-hand notation for $$f(x) = 1 \quad \forall x$$ ?

I've seen $f\equiv 1$ being used before, but found some some might (mis)interpret that as $f:=1$ (in the sense of definition), i.e., $f$ being the number $1$.

• I tend to interpret $\equiv$ in the way you want. Also, I usually don't take $:=$ to mean a definition, so much as an instance. E.g. $f:=1$ to me means that $f$ will represent $1,$ but it is not a definition of $f.$ Jul 27, 2012 at 20:30
• I also interpret $\equiv$ in the way you want. (I do take $:=$ to denote a definition.) Jul 27, 2012 at 20:47
• $A\triangleq B$ is sometimes okay, and $\newcommand\assign{\mathinner{:=}}A\assign B$ sometimes represent $A\gets B$ in context of computer programmng. Jul 28, 2012 at 14:29
• That's why the (sub)section notation is always a great idea at the beginning of any book or paper.
– user2468
Jul 29, 2012 at 1:01

Go ahead and use $\equiv$. To prevent any possibility of misunderstanding, you can use the word "constant" the first time this notation appears. As in "let $f$ be the constant function $f\equiv1$..."