I received the following equation. It is supposed to contain clues to something I have to solve. I am not familiar with the math symbols used here.
How do I read the following:
f: R → D, ∀d ∈ D, ∃!r ∈ R: f(r) = Lm = d
I received the following equation. It is supposed to contain clues to something I have to solve. I am not familiar with the math symbols used here.
How do I read the following:
f: R → D, ∀d ∈ D, ∃!r ∈ R: f(r) = Lm = d
It says that $f$ is a function from $R$ to $D$, and for each $d\in D$ there is exactly one $r\in R$ with the property that $f(r)=d$. I can’t help with the $Lm$: it isn’t a standard notation and appears to be something derived from the context.
The symbols $\forall$ and $\exists!$ are quantifiers meaning respectively ‘for each’ and ‘there exists exactly one’.
Assuming that by $R$ you mean $\mathbb R$, the set of real numbers:
$f\colon\mathbb R\to D$ means that $f$ is a function from the real numbers to a set $D$.
$\forall d\in D$ is read "For every $d$ which is an element of $D$",
$\exists!r\in\mathbb R$ is to say "Exists a unique real number $r$"
$: f(r) = Lm = d$ such that $f(r)=Lm$, which as Brian said is not a standard notation, and also $f(r)=d$.
This means that $f$ is such function that for every $d\in D$ there is exactly one $r$ such that $f(r)=d$. This means that every two numbers are mapped to two distinct elements of $D$; such $f$ is called injective. We also deduce that every $d\in D$ is $f(r)$ for some $r$, and such $f$ is called surjective. If a function is both injective and surjective we say that it is bijective, or that it is a bijection.